#72209703

order	15360
isoclinism	isoclinic class of #72209703
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂³×C₄⁴

Aliases

No aliases for this group.

Splittings

Fitting, socle

C₂⁸ ⋊ A₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
Fitting, socle, cosocle	C₂⁸	A₅
LCS	G
UCS	C₁

12679 conjugacy classes of subgroups; only the 8 normal subgroups are shown.

normal subgroups only

This group has 12679 conjugacy classes of subgroups — too many to draw. Only its 8 normal subgroups are shown.

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

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72210034, #72210043, #72219284, …

GAP

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

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