C₁₁×#2571 #13065409

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#2571

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

380 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 216 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)(12,13,16,14)(15,18,19,17)(21,23)(25,26)(28,29,32,35)(30,34,31,33);(13,14)(17,18)(20,21,24,23)(22,25,27,26)(28,30,32,31)(29,33,35,34);(12,14,16,13)(15,18,19,17)(20,22,24,27)(21,25,23,26)(28,29)(30,33)(31,34)(32,35);(12,15,16,19)(13,17,14,18)(20,23,24,21)(22,26,27,25)(28,31,32,30)(29,34,35,33)

Conjugacy classes & character table

418 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14656797, #14656802, #14656807, …
maximal subgroup of	C₁₁×#10351, C₁₁×#10352, C₁₁×#10353, …
maximal normal subgroup of	C₁₁×#10351, C₁₁×#10352, C₁₁×#10353, …
maximal quotient of	C₁₁×#13911, C₁₁×#13982, C₁₁×#14030, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1303);