C₁₁×#2379 #13065217

order	1408
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₁ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₁₁×#2379

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁴×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

520 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 264 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)(17,20)(18,22)(24,25)(26,30)(27,28)(29,31);(17,20)(21,23)(25,28)(26,31);(16,17,19,20)(18,21,22,23)(24,25)(26,29)(27,28)(30,31);(16,18)(17,21)(19,22)(20,23)(24,26,27,31)(25,29,28,30)

Conjugacy classes & character table

418 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14648128, #14648134, #14648152, …
maximal subgroup of	C₁₁×#8910, C₁₁×#8911, C₁₁×#8914, …
maximal normal subgroup of	C₁₁×#8910, C₁₁×#8911, C₁₁×#8914, …
maximal quotient of	C₁₁×#13829, C₁₁×#13831, C₁₁×#13832, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1111);