#72257366

order	61440
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂⁵×C₄²

Aliases

No aliases for this group.

Splittings

Fitting

C₂¹⁰ ⋊ A₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂²	#72209703
commutator, hypocenter	G	C₁
Fitting, cosocle	C₂¹⁰	A₅
socle	C₂⁶	#11757162
LCS	G
UCS	C₁ ◁ C₂²

Only the 16 normal subgroups are shown; non-normal subgroups are omitted.

normal subgroups only

Only the group's 16 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:

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

Conjugacy classes & character table

88 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((2,3,4)(5,8,9)(6,11,12)(7,13,14)(10,15,16)(17,18,19)(20,24,23)(21,22,25)(26,27,30)(28,33,29)(31,32,36)(34,38,35)(37,40,39), (2,5)(3,6)(4,7)(8,14)(9,11)(12,13)(18,21)(19,22)(23,28)(24,29)(26,31)(27,32)(34,37)(35,39), (2,3)(5,9)(6,11)(7,15)(10,13)(14,16)(17,18)(20,24)(22,25)(27,30)(28,33)(31,36)(34,38)(39,40), (1,2)(3,4)(5,10)(6,9)(7,8)(11,14)(12,15)(13,16), (17,20)(19,23)(21,26)(22,27)(28,34)(29,35)(32,37)(36,40));