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C22×C97⋊C3 #11923976

order1164
isoclinismisoclinic class of C97⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC22×C97⋊C3

Splittings

Fitting, socle, HallC22×C97 ⋊ C3
derived, SylowC97 ⋊ C22×C3

Subgroups

subgroupG/H
center, hypercenterC22C97⋊C3
commutator, cosocle, hypocenterC97C22×C3
FrattiniC1G
Fitting, socleC22×C97C3
LCSG ▷ C97
UCSC1 ◁ C22

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 101
transitive degreeμt(G) = 388

A minimal faithful permutation representation — 2 generators on 101 points:

(1,2)(6,7,9)(8,11,16)(10,14,13)(12,18,26)(15,21,23)(17,24,20)(19,28,39)(22,31,36)(25,34,33)(27,37,30)(29,41,55)(32,44,52)(35,47,49)(38,50,46)(40,53,43)(42,57,63)(45,59,70)(48,62,67)(51,65,64)(54,68,61)(56,71,58)(60,75,77)(66,79,81)(69,82,78)(72,84,76)(73,80,74)(83,90,89)(85,92,88)(86,91,87)(93,97,96)(94,98,95)(99,101,100);(3,4)(5,6,8,12,19,29,42,44,18,27,38,51,66,80,55,70,57,73,86,94,99,101,92,68,37,16,23,33,46,61,76,87,79,47,21,7,10,15,22,32,45,60,59,28,40,54,69,83,91,71,39,52,67,81,89,96,100,97,82,50,24,9,13,20,30,43,58,74,62,31,11,17,25,35,48,63,77,75,41,56,72,85,93,98,84,53,26,36,49,64,78,88,95,90,65,34,14)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×C97⋊C3, C2×D3×C97⋊C3, C22×C3×C97⋊C3, …
maximal normal subgroup ofA4×C97⋊C3, C22×C3×C97⋊C3, C22×C11×C97⋊C3, …
maximal quotient ofC22×C97⋊C9, C2×D3×C97⋊C3, C22×C3×C97⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1164, 12);