C₂×C₁₁×#1655 #14596171

order	2816
nilpotency class	3
isoclinism	isoclinic class of #1655
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₁₁×#1655

Subgroups

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

1330 conjugacy classes of subgroups; only the 238 normal subgroups are shown.

normal subgroups only

This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 238 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) = 29
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

440 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 11966);