#72266682

order	61440
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

Splittings

Fitting

C₂¹⁰ ⋊ A₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂²	#72209715
commutator, hypocenter	G	C₁
Fitting, cosocle	C₂¹⁰	A₅
socle	C₂⁶	#11757162
LCS	G
UCS	C₁ ◁ C₂²

Only the 13 normal subgroups are shown; non-normal subgroups are omitted.

normal subgroups only

Only the group's 13 normal subgroups are shown; non-normal subgroups are omitted.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

GAP

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

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