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C2×C11×#401 #13065238

order1408
nilpotency class2
isoclinismisoclinic class of #392
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C25

Aliases

direct productC2×C11×#401

Subgroups

subgroupG/H
center, socle, prime radicalC24×C11C23
commutator, Frattini, cosocleC23C24×C11
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C11 ◁ G

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 1408

A minimal faithful permutation representation — 4 generators on 37 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37);(5,9)(7,10)(12,15)(16,17)(19,20,22,24)(21,25,26,23);(3,4,6,8)(5,10,9,7)(11,12,14,15)(13,17,18,16)(19,20)(21,25)(22,24)(23,26);(3,5)(4,7)(6,9)(8,10)(11,13,14,18)(12,16,15,17)(19,21,22,26)(20,23,24,25)

Conjugacy classes & character table

484 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofDic11×#401, #14680092, #14680913, …
maximal subgroup ofC4×C11×#401, C11×#14251, C11×#14333, …
maximal normal subgroup ofC4×C11×#401, C11×#14251, C11×#14333, …
maximal quotient ofC2×C11×#1443, C4×C11×#401, C11×C22⋊#401, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1132);