C₁₁×#2815 #13065653

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₁×#2815

Subgroups

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

644 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 184 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)(17,20)(21,23)(24,25,27,28)(26,29,31,30);(13,15)(17,20)(18,22)(25,28)(29,30);(12,13)(14,15)(16,17)(18,21)(19,20)(22,23)(24,25)(26,30)(27,28)(29,31);(16,18)(17,21)(19,22)(20,23)(24,26,27,31)(25,29,28,30)

Conjugacy classes & character table

286 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14654405, #14654422, #14665826, …
maximal subgroup of	C₁₁×#9980, C₁₁×#9983, C₁₁×#12094, …
maximal normal subgroup of	C₁₁×#9980, C₁₁×#9983, C₁₁×#12094, …
maximal quotient of	C₁₁×#14621, C₁₁×#14623, C₁₁×#14630, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1547);