C₁₁×#11990 #14589183

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11989
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#11990

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₁	#1551
commutator	C₄²	C₂²×C₄×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₂³×C₁₁	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₁₁×#405 ◁ G

268 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 75
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 3 generators on 75 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,22,17,21,35,47,18,24,36,50,38,23,51,49)(14,25,27,53,28,42,57,67,29,41,58,48,37,19,34,40)(15,30,32,59,33,20,43,44,31,46,60,72,61,45,69,71)(26,39,55,65,56,52,73,74,54,66,68,75,63,64,62,70);(12,14,18,29)(13,19,24,42)(15,26,31,54)(16,34,36,57)(17,37,38,28)(20,39,45,66)(21,41,23,25)(22,48,50,53)(27,35,58,51)(30,52,46,64)(32,62,60,73)(33,63,61,56)(40,47,67,49)(43,68,69,55)(44,70,71,74)(59,65,72,75);(12,15)(13,20,24,45)(14,26)(16,32)(17,33)(18,31)(19,39,42,66)(21,46,23,30)(22,44,50,71)(25,52,41,64)(27,55)(28,56)(29,54)(34,62)(35,43)(36,60)(37,63)(38,61)(40,65,67,75)(47,72,49,59)(48,70,53,74)(51,69)(57,73)(58,68)

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, 4978);