C₁₁×#11416 #14588609

order	2816
nilpotency class	2
isoclinism	isoclinic class of #7855
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₁×#11416

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×#97
prime radical	C₂³×C₁₁	#97
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

228 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 150 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)(12,13,15,18,16,19,22,25)(14,17,21,24,20,23,26,27)(28,29)(30,38,39,50)(31,42)(32,37)(33,35)(34,41,46,53)(36,44)(40,54,52,51)(43,57)(45,48)(47,59,56,55)(49,58);(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27)(28,30,31,40,32,41,43,55,33,39,44,52,45,53,58,59)(29,34,36,47,37,38,49,51,35,46,42,56,48,50,57,54);(14,20)(17,23)(21,26)(24,27)(29,35)(34,46)(36,42)(37,48)(38,50)(47,56)(49,57)(51,54)

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4404);