#72209609

order	4860
isoclinism	isoclinic class of #72209609
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	G	C₁
Frattini, Fitting, socle, cosocle	C₃⁴	A₅
LCS	G
UCS	C₁

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

(1,2)(3,7)(4,8)(5,9)(6,13)(10,19)(11,17)(12,18)(14,22)(15,21)(16,25)(20,30)(23,29)(24,32)(26,35)(27,36)(28,37)(31,40)(33,41)(34,44)(38,46)(39,49)(42,53)(43,54)(45,48)(47,55)(50,51)(52,58)(56,59)(57,60);(2,5,10,7,11,14,8,12,6)(9,15,16)(13,20,29,19,28,32,22,31,21)(17,23,26)(18,24,27)(25,33,34)(30,38,47,37,44,50,40,48,39)(35,42,45)(36,43,46)(41,51,57,53,49,56,54,55,52)(58,59,60);(1,3,4)(6,10,14)(9,17,18)(13,19,22)(15,23,24)(20,28,31)(30,37,40)(33,42,43)(34,45,46)(39,47,50)(49,55,51)(58,60,59);(1,3,4)(2,7,8)(15,23,24)(16,26,27)(20,28,31)(21,29,32)(25,35,36)(30,37,40)(34,45,46)(38,44,48)(52,57,56)(58,60,59);(1,3,4)(5,11,12)(9,17,18)(13,19,22)(16,26,27)(21,29,32)(25,35,36)(33,42,43)(38,44,48)(39,47,50)(41,53,54)(58,60,59);(2,7,8)(5,11,12)(6,10,14)(13,19,22)(20,28,31)(21,29,32)(30,37,40)(38,44,48)(39,47,50)(41,53,54)(49,55,51)(52,57,56)

Conjugacy classes & character table

24 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72209636

GAP

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

gap> G := Group((1,2)(3,7)(4,8)(5,9)(6,13)(10,19)(11,17)(12,18)(14,22)(15,21)(16,25)(20,30)(23,29)(24,32)(26,35)(27,36)(28,37)(31,40)(33,41)(34,44)(38,46)(39,49)(42,53)(43,54)(45,48)(47,55)(50,51)(52,58)(56,59)(57,60), (2,5,10,7,11,14,8,12,6)(9,15,16)(13,20,29,19,28,32,22,31,21)(17,23,26)(18,24,27)(25,33,34)(30,38,47,37,44,50,40,48,39)(35,42,45)(36,43,46)(41,51,57,53,49,56,54,55,52)(58,59,60), (1,3,4)(6,10,14)(9,17,18)(13,19,22)(15,23,24)(20,28,31)(30,37,40)(33,42,43)(34,45,46)(39,47,50)(49,55,51)(58,60,59), (1,3,4)(2,7,8)(15,23,24)(16,26,27)(20,28,31)(21,29,32)(25,35,36)(30,37,40)(34,45,46)(38,44,48)(52,57,56)(58,60,59), (1,3,4)(5,11,12)(9,17,18)(13,19,22)(16,26,27)(21,29,32)(25,35,36)(33,42,43)(38,44,48)(39,47,50)(41,53,54)(58,60,59), (2,7,8)(5,11,12)(6,10,14)(13,19,22)(20,28,31)(21,29,32)(30,37,40)(38,44,48)(39,47,50)(41,53,54)(49,55,51)(52,57,56));