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C22×#63271 #11764015

order1092
isoclinismisoclinic class of #63271
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC22×#63271

Splittings

Fitting, socle, HallC22×C7×C13 ⋊ C3
derived, HallC7×C13 ⋊ C22×C3
HallC22×C13 ⋊ ΓL(1,𝔽8)
HallC22×C7 ⋊ C13⋊C3
SylowC13 ⋊ C22×ΓL(1,𝔽8)
SylowC7 ⋊ C22×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC22#63271
commutator, cosocle, hypocenterC7×C13C22×C3
FrattiniC1G
Fitting, socleC22×C7×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C22

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×ΓL(1,𝔽8)×C13⋊C3, A4×#63271, #63271⋊A4, …
maximal normal subgroup ofC22×ΓL(1,𝔽8)×C13⋊C3, A4×#63271, #63271⋊A4, …
maximal quotient ofC22×#11717942, C2×D3×#63271, C22×C3×#63271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1092, 63);