Finite Group Databasebeta

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C7×C22⋊((C43⋊C3)⋊C7) #38760397

order25284
automorphism?
homologyAbelianization (H1) = C3×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC7×C22⋊((C43⋊C3)⋊C7)
unambiguous semidirect productC22⋊(C7×(C43⋊C3)⋊C7)
unambiguous semidirect product(C43⋊C7)⋊(C7×A4)
unambiguous semidirect product(C22⋊(C43⋊C3))⋊C72
unambiguous semidirect product(C7×C22⋊(C43⋊C3))⋊C7

Splittings

Fitting, socleC22×C7×C43 ⋊ C3×C7
derived, HallC22×C43 ⋊ C3×C72
HallC22×C7×C43⋊C7 ⋊ C3
HallC7×C43⋊C7 ⋊ A4
HallC22⋊(C43⋊C3) ⋊ C72
SylowC43 ⋊ C72×A4
SylowC22 ⋊ C7×(C43⋊C3)⋊C7

Subgroups

subgroupG/H
center, hypercenterC7C22⋊((C43⋊C3)⋊C7)
commutator, cosocle, hypocenterC22×C43C3×C72
FrattiniC1G
Fitting, socleC22×C7×C43C3×C7
LCSG ▷ C22×C43
UCSC1 ◁ C7

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1204

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 204);