C₁₁×#7043 #14584236

order	2816
nilpotency class	3
isoclinism	isoclinic class of #7035
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₁×#7043

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	#95
commutator	C₂²×C₄	C₄²×C₁₁
Frattini, cosocle	C₄³	C₂²×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄³×C₁₁ ◁ G

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

normal subgroups only

This group has 284 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) = 35
transitive degree	μ_t(G) = 2816

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18,17,14,15,19)(21,24)(22,26)(29,33,34,35);(12,14,17,13)(15,18,16,19)(20,21,22,25,23,24,26,27)(28,29,31,33,32,34,30,35)

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, 31);