C₁₁×#11497 #14588690

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₁×#11497

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

288 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 130 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)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)(28,29,33,39,35,38,48,37,34,40,47,56,32,49,31,46)(30,41,44,57,43,36,51,53,45,55,59,52,50,54,42,58);(12,14,16,22)(13,17,19,20)(15,21,23,27)(18,24,25,26)(28,30,34,45)(29,36,40,54)(31,42,48,51)(32,50,35,43)(33,44,47,59)(37,52,46,57)(38,55,49,41)(39,53,56,58);(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26)(28,31,32,47,34,48,35,33)(29,37,49,39,40,46,38,56)(30,42,50,59,45,51,43,44)(36,52,41,53,54,57,55,58)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4485);