C₁₁×#2860 #13065698

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#2860

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

516 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 216 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)(13,15)(17,18)(21,22)(26,29)(27,31);(16,17,20,18)(19,21,23,22)(24,25,28,30)(26,27,29,31);(12,13,14,15)(16,18,20,17)(19,22,23,21)(24,26,28,29)(25,27,30,31);(16,19,20,23)(17,21,18,22)(24,27)(25,29)(26,30)(28,31)

Conjugacy classes & character table

484 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14642159, #14642187, #14642251, …
maximal subgroup of	C₁₁×#7666, C₁₁×#7672, C₁₁×#7686, …
maximal normal subgroup of	C₁₁×#7666, C₁₁×#7672, C₁₁×#7686, …
maximal quotient of	C₁₁×#14688, C₁₁×#14699, C₁₁×#14700, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1592);