#72257402

order	61440
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂³×C₄³

Aliases

No aliases for this group.

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

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