C₁₁×#2629 #13065467

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#2629

Subgroups

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

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

normal subgroups only

This group has 472 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)(16,17)(18,20)(19,21)(22,23)(24,25,28,27)(26,30,31,29);(13,15)(17,18)(21,22)(24,26)(25,29)(27,30)(28,31);(12,13)(14,15)(16,18,20,17)(19,21,23,22)(24,26)(25,30)(27,29)(28,31);(16,19,20,23)(17,21,18,22)(24,27,28,25)(26,30,31,29)

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14795127, #14795157, #14795187, …
maximal subgroup of	C₁₁×#24713, C₁₁×#24715, C₁₁×#24717, …
maximal normal subgroup of	C₁₁×#24713, C₁₁×#24715, C₁₁×#24717, …
maximal quotient of	C₁₁×#14264, C₁₁×#14266, C₁₁×#14276, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1361);