C₁₁×#23895 #14601088

order	2816
nilpotency class	3
isoclinism	isoclinic class of #23895
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₁×#23895

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#2403
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₁
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂⁴×C₁₁ ◁ G

2002 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 2002 conjugacy classes of subgroups — too many to draw. Only its 282 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 4 generators on 27 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 16883);