C₁₁×#12511 #14589704

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₁×#12511

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

260 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 59
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,23)(16,18)(17,21)(19,24)(22,26)(25,27)(28,29)(30,44)(31,37)(32,52)(33,54)(34,42)(35,41)(36,43)(38,49)(39,45)(40,53)(46,56)(47,55)(48,59)(50,57)(51,58);(12,14,15,21,16,22,24,27)(13,17,19,20,18,25,23,26)(28,30,45,50,34,47,53,51,36,49,33,46,35,48,32,31)(29,37,52,59,41,56,54,38,43,58,40,55,42,57,39,44);(13,18)(17,25)(19,23)(20,26)(28,31,32,48,35,46,33,49,36,51,53,47,34,50,45,30)(29,38,39,56,42,59,40,37,43,44,54,57,41,55,52,58)

Conjugacy classes & character table

770 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5499);