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C2×C3⋊(C3⋊(D29⋊C7)) #20300620

order7308
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊(C3⋊(D29⋊C7))
unambiguous semidirect product(C2×C3)⋊(C3⋊(D29⋊C7))
unambiguous semidirect product(C2×C29⋊C7)⋊(C3⋊D3)
unambiguous semidirect product(C2×C3⋊D87)⋊C7

Splittings

Fitting, socleC2×C32×C29 ⋊ C2×C7
derived, HallC32×C29 ⋊ C22×C7
HallC32×C29⋊C7 ⋊ C22
HallC2×C3⋊D87 ⋊ C7
HallC29⋊C7 ⋊ C2×C3⋊D3
SylowC29 ⋊ C2×C7×C3⋊D3
SylowC32 ⋊ C2×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C3⋊(D29⋊C7))
commutator, hypocenterC32×C29C22×C7
FrattiniC1G
Fitting, socleC2×C32×C29C2×C7
LCSG ▷ C32×C29
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C3⋊(C3⋊(D29⋊C7)), C2×C5×C3⋊(C3⋊(D29⋊C7)), C2×C3⋊(C3⋊(C5⋊(D29⋊C7)))
maximal normal subgroup ofC2×C5×C3⋊(C3⋊(D29⋊C7))
maximal quotient ofD5×C3⋊(C3⋊(D29⋊C7)), C2×C5×C3⋊(C3⋊(D29⋊C7)), C2×C3⋊(C3⋊(C5⋊(D29⋊C7)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 95);