C₁₁×#2843 #13065681

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₁×#2843

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

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

normal subgroups only

This group has 348 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) = 35
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

286 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14666362, #14666846, D₁₁×#2843, …
maximal subgroup of	C₁₁×#12183, C₁₁×#12259, C₂×C₁₁×#2843, …
maximal normal subgroup of	C₁₁×#12183, C₁₁×#12259, C₂×C₁₁×#2843, …
maximal quotient of	C₁₁×#14638, C₁₁×#14639, C₁₁×#14640, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1575);