#72257380

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, socle, hypercenter	C₂²	#72209703
commutator, hypocenter	G	C₁
Fitting, cosocle	C₂¹⁰	A₅
LCS	G
UCS	C₁ ◁ C₂²

Only the 15 normal subgroups are shown; non-normal subgroups are omitted.

normal subgroups only

Only the group's 15 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)(4,10,9)(5,7,11)(6,8,13)(12,14,19)(15,20,18)(16,22,17)(21,24,23);(2,5)(3,7)(6,12)(8,14)(9,16)(10,17)(15,21)(18,23);(1,2)(4,10)(6,13)(7,11)(14,19)(16,22)(18,20)(21,24);(2,6)(3,8)(5,12)(7,14)(9,15)(10,18)(16,21)(17,23);(1,4)(3,9)(8,15)(13,20)

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((1,2,3)(4,10,9)(5,7,11)(6,8,13)(12,14,19)(15,20,18)(16,22,17)(21,24,23), (2,5)(3,7)(6,12)(8,14)(9,16)(10,17)(15,21)(18,23), (1,2)(4,10)(6,13)(7,11)(14,19)(16,22)(18,20)(21,24), (2,6)(3,8)(5,12)(7,14)(9,15)(10,18)(16,21)(17,23), (1,4)(3,9)(8,15)(13,20));