C₁₁×#2640 #13065478

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₁×#2640

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

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

normal subgroups only

This group has 500 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) = 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)(12,13,14,15)(16,17,20,23)(18,19,22,21)(26,30)(28,31);(12,13,14,15)(16,18,20,22)(17,21,23,19)(24,25,27,29)(26,28,30,31);(12,13)(14,15)(16,18)(17,21)(19,23)(20,22)(24,26)(25,28)(27,30)(29,31);(16,19,20,21)(17,22,23,18)

Conjugacy classes & character table

352 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14655129, #14655143, #14655185, …
maximal subgroup of	C₁₁×#10090, C₁₁×#10092, C₁₁×#10098, …
maximal normal subgroup of	C₁₁×#10090, C₁₁×#10092, C₁₁×#10098, …
maximal quotient of	C₁₁×#14260, C₁₁×#14261, C₁₁×#14273, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1372);