C₁₁×#12889 #14590082

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#12889

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

310 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 55
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 3 generators on 55 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5877);