C₁₁×#2642 #13065480

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₁×#2642

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

416 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 39
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(18,22)(20,23)(25,29)(30,32)(31,37)(38,39);(12,13,14,15)(16,17,19,21)(18,20,22,23)(24,25)(26,32)(27,31)(28,29)(30,34)(33,39)(35,38)(36,37);(12,13)(14,15)(16,18)(17,20)(19,22)(21,23)(24,26,28,34)(25,30,29,32)(27,35,36,33)(31,39,37,38);(24,27,28,36)(25,31,29,37)(26,33,34,35)(30,38,32,39)

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14655164, #14655220, #14728996, …
maximal subgroup of	C₁₁×#10095, C₁₁×#10103, C₁₁×#18441, …
maximal normal subgroup of	C₁₁×#10095, C₁₁×#10103, C₁₁×#18441, …
maximal quotient of	C₁₁×#14261, C₁₁×#14274, C₁₁×#14283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1374);