C₁₁×#8101 #14585294

order	2816
nilpotency class	3
isoclinism	isoclinic class of #8101
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₁×#8101

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#95
commutator	C₂³	C₂×C₄²×C₁₁
Frattini, cosocle	C₂⁵	C₂³×C₁₁
prime radical	C₂⁶×C₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁶×C₁₁ ◁ G

2414 conjugacy classes of subgroups; only the 278 normal subgroups are shown.

normal subgroups only

This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 278 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 — 3 generators on 27 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1089);