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C2×C9⋊(D29⋊C7) #20300548

order7308
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9⋊(D29⋊C7)
unambiguous semidirect product(C2×C9)⋊(D29⋊C7)
unambiguous semidirect product(C2×C29⋊C7)⋊D9
unambiguous semidirect product(C2×D261)⋊C7

Splittings

FittingC2×C9×C29 ⋊ C2×C7
derived, HallC9×C29 ⋊ C22×C7
HallC9×C29⋊C7 ⋊ C22
HallC2×D261 ⋊ C7
HallC29⋊C7 ⋊ C2×D9
SylowC29 ⋊ C2×C7×D9
SylowC9 ⋊ C2×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2C9⋊(D29⋊C7)
commutator, hypocenterC9×C29C22×C7
FrattiniC3C2×C3⋊(D29⋊C7)
FittingC2×C9×C29C2×C7
socleC2×C3×C29D3×C7
LCSG ▷ C9×C29
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C9⋊(D29⋊C7), C2×C5×C9⋊(D29⋊C7), C2×C5⋊(C9⋊(D29⋊C7))
maximal normal subgroup ofC2×C5×C9⋊(D29⋊C7)
maximal quotient ofD5×C9⋊(D29⋊C7), C2×C5×C9⋊(D29⋊C7), C2×C5⋊(C9⋊(D29⋊C7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 23);