#72209605

order	3840
isoclinism	isoclinic class of #72209605
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle, hypercenter	C₂	#14515303
commutator, hypocenter	G	C₁
Frattini, Fitting, cosocle	C₂⁴×C₄	A₅
LCS	G
UCS	C₁ ◁ C₂

99 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

(1,2,5,8,7,9,6,3)(4,11,10,15,14,18,13,12)(16,23,19,29,25,31,21,24)(17,26,22,32,28,30,20,27)(33,37,34,39,36,40,35,38)(41,44,43,48,47,46,45,42);(1,4,2)(3,6,10)(5,13,8)(7,14,9)(11,16,17)(12,19,20)(15,21,22)(18,25,28)(23,27,33)(24,26,34)(29,30,35)(31,32,36)(37,41,42)(38,43,44)(39,45,46)(40,47,48);(1,5,7,6)(2,8,9,3)(4,10,14,13)(11,15,18,12)(16,19,25,21)(17,22,28,20)(23,29,31,24)(26,32,30,27)(33,34,36,35)(37,39,40,38)(41,43,47,45)(42,44,48,46);(2,9)(3,8)(4,14)(10,13)(11,18)(12,15)(16,25)(19,21)(23,31)(24,29)(33,36)(34,35)(37,40)(38,39)(41,47)(43,45);(1,7)(2,9)(3,8)(4,14)(5,6)(10,13)(17,28)(20,22)(26,30)(27,32)(37,40)(38,39)(41,47)(42,48)(43,45)(44,46);(1,7)(4,14)(5,6)(10,13)(11,18)(12,15)(16,25)(19,21)(23,31)(24,29)(33,36)(34,35)(37,40)(38,39)(42,48)(44,46);(1,7)(2,9)(3,8)(5,6)(11,18)(12,15)(17,28)(20,22)(26,30)(27,32)(33,36)(34,35)(41,47)(42,48)(43,45)(44,46);(1,7)(2,9)(3,8)(4,14)(5,6)(10,13)(11,18)(12,15)(16,25)(17,28)(19,21)(20,22)(23,31)(24,29)(26,30)(27,32)(33,36)(34,35)(37,40)(38,39)(41,47)(42,48)(43,45)(44,46)

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72240076, #72268920
maximal quotient of	#72237324, #72237341, #72240596, …

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,2,5,8,7,9,6,3)(4,11,10,15,14,18,13,12)(16,23,19,29,25,31,21,24)(17,26,22,32,28,30,20,27)(33,37,34,39,36,40,35,38)(41,44,43,48,47,46,45,42), (1,4,2)(3,6,10)(5,13,8)(7,14,9)(11,16,17)(12,19,20)(15,21,22)(18,25,28)(23,27,33)(24,26,34)(29,30,35)(31,32,36)(37,41,42)(38,43,44)(39,45,46)(40,47,48), (1,5,7,6)(2,8,9,3)(4,10,14,13)(11,15,18,12)(16,19,25,21)(17,22,28,20)(23,29,31,24)(26,32,30,27)(33,34,36,35)(37,39,40,38)(41,43,47,45)(42,44,48,46), (2,9)(3,8)(4,14)(10,13)(11,18)(12,15)(16,25)(19,21)(23,31)(24,29)(33,36)(34,35)(37,40)(38,39)(41,47)(43,45), (1,7)(2,9)(3,8)(4,14)(5,6)(10,13)(17,28)(20,22)(26,30)(27,32)(37,40)(38,39)(41,47)(42,48)(43,45)(44,46), (1,7)(4,14)(5,6)(10,13)(11,18)(12,15)(16,25)(19,21)(23,31)(24,29)(33,36)(34,35)(37,40)(38,39)(42,48)(44,46), (1,7)(2,9)(3,8)(5,6)(11,18)(12,15)(17,28)(20,22)(26,30)(27,32)(33,36)(34,35)(41,47)(42,48)(43,45)(44,46), (1,7)(2,9)(3,8)(4,14)(5,6)(10,13)(11,18)(12,15)(16,25)(17,28)(19,21)(20,22)(23,31)(24,29)(26,30)(27,32)(33,36)(34,35)(37,40)(38,39)(41,47)(42,48)(43,45)(44,46));