#72209637

order	9720
isoclinism	isoclinic class of #72209637
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₃²

Aliases

No aliases for this group.

Splittings

Fitting, socle

C₃⁴ ⋊ SL(2,𝔽₅)

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
Fitting, socle	C₃⁴	SL(2,𝔽₅)
cosocle	C₃⋊(C₃⋊(C₃⋊D₃))	A₅
LCS	G
UCS	C₁

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

15 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72227932
maximal quotient of	#72209953, #72209956

GAP

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

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