C₁₁×#11758 #14588951

order	2816
nilpotency class	4
isoclinism	isoclinic class of #11757
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₁ · Schur multiplier (H₂) = C₄²

Aliases

direct product

C₁₁×#11758

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₁
prime radical	C₁₁×#392	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

486 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 35
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 35 points:

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

Conjugacy classes & character table

407 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 4746);