C₁₁×#11412 #14588605

order	2816
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₁ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₁×#11412

Subgroups

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

260 conjugacy classes of subgroups; only the 190 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 190 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)(30,34)(31,36)(32,37)(33,35)(38,45)(39,46)(40,44)(41,49)(42,47)(43,48)(50,56)(51,54)(52,55)(53,57)(58,59);(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27)(28,30,31,38,32,39,41,50,33,40,42,51,43,52,53,58)(29,34,36,45,37,46,49,56,35,44,47,54,48,55,57,59);(14,20)(17,23)(21,26)(24,27)(29,35)(34,44)(36,47)(37,48)(45,54)(46,55)(49,57)(56,59)

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4400);