C₁₁×#11549 #14588742

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11549
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₁×#11549

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₁
prime radical	C₂×C₁₁×#121	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂⁴×C₁₁ ◁ C₂²×C₁₁×C₄⋊C₄ ◁ G

496 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 704

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4537);