C₁₁×#2383 #13065221

order	1408
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#2383

Subgroups

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

456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 31
transitive degree	μ_t(G) = 704

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

418 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₁×#2383, #14916442, #14916460, …
maximal subgroup of	C₂×C₁₁×#2383, C₁₁×#34350, C₄×C₁₁×#560, …
maximal normal subgroup of	C₂×C₁₁×#2383, C₁₁×#34350, C₄×C₁₁×#560, …
maximal quotient of	C₁₁×#13830, C₁₁×#13831, C₁₁×#13833, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1115);