C₁₁×#19008 #14596201

order	2816
nilpotency class	3
isoclinism	isoclinic class of #18992
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#19008

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

786 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 222 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 — 4 generators on 59 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 11996);