C₂×C₁₁×#2842 #14613865

order	2816
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₁ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₁₁×#2842

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂⁶×C₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ G

3294 conjugacy classes of subgroups; only the 974 normal subgroups are shown.

normal subgroups only

This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 974 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) = 37
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 5 generators on 37 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37);(4,7)(8,10)(11,12)(13,15)(14,16)(17,18)(21,25)(23,26);(5,9)(8,10)(12,13)(16,17)(19,20,22,24)(21,26,25,23);(3,4)(5,8)(6,7)(9,10)(11,13,15,12)(14,16,18,17)(19,21,22,25)(20,23,24,26);(3,5)(4,8)(6,9)(7,10)(11,14)(12,16)(13,17)(15,18)(19,20)(21,23)(22,24)(25,26)

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, 29660);