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C7×C3⋊(D67⋊C3) #22554755

order8442
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(D67⋊C3)
unambiguous semidirect productC3⋊(C7×D67⋊C3)
unambiguous semidirect product(C67⋊C3)⋊(D3×C7)
unambiguous semidirect productD201⋊(C3×C7)

Splittings

Fitting, socleC3×C7×C67 ⋊ C2×C3
derivedC3×C67 ⋊ C2×C3×C7
HallC3×C7×C67⋊C3 ⋊ C2
HallC3×C67⋊C3 ⋊ C2×C7
HallC7×C67 ⋊ C3×D3
SylowC67 ⋊ C3×D3×C7

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(D67⋊C3)
commutator, hypocenterC3×C67C2×C3×C7
FrattiniC1G
Fitting, socleC3×C7×C67C2×C3
LCSG ▷ C3×C67
UCSC1 ◁ C7

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

294 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C7×D67⋊C3, D7×C3⋊(D67⋊C3), (C3⋊(D67⋊C3))⋊D7, …
maximal normal subgroup ofD3×C7×D67⋊C3, D7×C3⋊(D67⋊C3), (C3⋊(D67⋊C3))⋊D7, …
maximal quotient ofC7×C3⋊((C67⋊C3)⋊C4), C2×C7×C3⋊(D67⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8442, 42);