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C2×C3×C3⋊(D29⋊C7) #20300618

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

Aliases

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

Splittings

Fitting, socleC2×C32×C29 ⋊ C2×C7
derivedC3×C29 ⋊ C22×C3×C7
HallC32×C29⋊C7 ⋊ C22
HallC2×C3×D87 ⋊ C7
HallC32×C29 ⋊ C22×C7
HallC29⋊C7 ⋊ C2×C3×D3
SylowC29 ⋊ C2×C3×D3×C7
SylowC32 ⋊ C2×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D29⋊C7)
commutator, hypocenterC3×C29C22×C3×C7
FrattiniC1G
Fitting, socleC2×C32×C29C2×C7
LCSG ▷ C3×C29
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

162 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×C3⋊(D29⋊C7), C2×C3×C5×C3⋊(D29⋊C7), C2×C3×C3⋊(C5⋊(D29⋊C7))
maximal normal subgroup ofC2×C3×C5×C3⋊(D29⋊C7)
maximal quotient ofC3×D5×C3⋊(D29⋊C7), C2×C3×C5×C3⋊(D29⋊C7), C2×C3×C3⋊(C5⋊(D29⋊C7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 93);