C₁₁×#2734 #13065572

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#2734

Subgroups

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

456 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 1408

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

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

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14642513, #14642601, #14642657, …
maximal subgroup of	C₁₁×#7741, C₁₁×#7757, C₁₁×#7766, …
maximal normal subgroup of	C₁₁×#7741, C₁₁×#7757, C₁₁×#7766, …
maximal quotient of	C₁₁×#14406, C₁₁×#14441, C₁₁×#14450, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1466);