#72209643

order	10752
isoclinism	isoclinic class of #72209643
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

Fitting, socle

C₂⁶ ⋊ GL(3,𝔽₂)

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
Fitting, socle, cosocle	C₂⁶	GL(3,𝔽₂)
LCS	G
UCS	C₁

1730 conjugacy classes of subgroups; only the 6 normal subgroups are shown.

normal subgroups only

This group has 1730 conjugacy classes of subgroups — too many to draw. Only its 6 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)(3,7)(10,12)(11,15);(2,3,5)(6,8,7)(10,11,13)(14,16,15);(1,2)(3,5)(4,6)(7,8);(1,3)(2,5)(4,8)(6,7);(1,4)(2,6)(3,8)(5,7);(9,10)(11,13)(12,14)(15,16);(9,11)(10,13)(12,16)(14,15);(9,12)(10,14)(11,16)(13,15)

Conjugacy classes & character table

25 conjugacy classes — view the full character table.

Relationships

maximal quotient of

#72209765, #72209775

GAP

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

gap> G := Group((2,4)(3,7)(10,12)(11,15), (2,3,5)(6,8,7)(10,11,13)(14,16,15), (1,2)(3,5)(4,6)(7,8), (1,3)(2,5)(4,8)(6,7), (1,4)(2,6)(3,8)(5,7), (9,10)(11,13)(12,14)(15,16), (9,11)(10,13)(12,16)(14,15), (9,12)(10,14)(11,16)(13,15));