C₂×C₁₁×#2203 #14610756

order	2816
nilpotency class	4
isoclinism	isoclinic class of #2202
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₁×#2203

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#454	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂³×C₁₁ ◁ C₂²×Q₈×C₁₁ ◁ G

1092 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 45
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45);(3,4)(5,14)(6,18)(7,10)(8,13)(9,15)(11,21)(12,23)(16,31)(17,29)(19,27)(20,28)(22,32)(24,30)(25,33)(26,34);(3,5,8,17)(4,9,13,27)(6,19,21,15)(7,22,23,16)(10,25,12,26)(11,29,18,14)(20,33,24,34)(28,31,30,32);(4,10)(7,23)(9,25)(11,30)(12,13)(14,31)(16,22)(18,28)(20,24)(26,27)(29,32)(33,34)

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, 26551);