C₁₁×#2551 #13065389

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₁×#2551

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

556 conjugacy classes of subgroups; only the 280 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 280 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) = 27
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 4 generators on 27 points:

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

Conjugacy classes & character table

418 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14656780, #14656785, #14656790, …
maximal subgroup of	C₁₁×#10348, C₁₁×#10349, C₁₁×#10350, …
maximal normal subgroup of	C₁₁×#10348, C₁₁×#10349, C₁₁×#10350, …
maximal quotient of	C₁₁×#13910, C₁₁×#14005, C₁₁×#14053, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1283);