#72209715

order	15360
isoclinism	isoclinic class of #72209715
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂²×C₄²

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

10694 conjugacy classes of subgroups; only the 5 normal subgroups are shown.

normal subgroups only

This group has 10694 conjugacy classes of subgroups — too many to draw. Only its 5 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)(17,18)(19,22)(21,24)(25,26);(2,6,7)(3,11,12)(4,14,5)(8,9,13)(10,15,16)(18,20,21)(22,23,25);(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);(17,19)(20,23)(21,25)(24,26);(17,19)(18,22)(21,25)(24,26);(17,19)(18,22)(20,23)(24,26);(18,22)(20,23)(21,25)(24,26)

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72211634, #72212895, #72213263, …

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