#72209622

order	7560
isoclinism	isoclinic class of #72209622
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, Fitting, socle, cosocle, hypercenter	C₃	A₇
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁ ◁ C₃

77 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

23 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72209688

GAP

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

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