C₁₁×#12310 #14589503

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12310
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#12310

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1619
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

406 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 78 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)(13,17)(14,21)(15,23)(18,22)(19,26)(20,25)(24,27);(14,21)(15,23)(17,22)(18,20)(24,27)(25,26);(12,13)(14,22)(15,18)(16,19)(17,21)(20,23)(24,25)(26,27)

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₁×#12310, #72269599
maximal subgroup of	D₁₁×#12310, C₁₁×#489347, #72269599
maximal normal subgroup of	D₁₁×#12310, C₁₁×#489347, #72269599

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5298);