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C22×C7×C13⋊C3 #11764013

order1092
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C7×C13⋊C3

Splittings

Fitting, socle, HallC22×C7×C13 ⋊ C3
derived, SylowC13 ⋊ C22×C3×C7
HallC7×C13 ⋊ C22×C3
HallC22×C13 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC22×C7C13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C7
FrattiniC1G
Fitting, socleC22×C7×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 364

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2)(5,6,7,8,9,10,11)(13,14,16)(15,18,21)(17,20,19)(22,24,23);(3,4)(12,13,15,14,17,21,18,22,24,16,19,23,20)

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×ΓL(1,𝔽8)×C13⋊C3, C7×A4×C13⋊C3, C13⋊C3×C22⋊ΓL(1,𝔽8), …
maximal normal subgroup ofC22×ΓL(1,𝔽8)×C13⋊C3, C7×A4×C13⋊C3, C13⋊C3×C22⋊ΓL(1,𝔽8), …
maximal quotient ofC22×C7×C13⋊C9, C2×D3×C7×C13⋊C3, C22×C3×C7×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1092, 61);