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C7×C3⋊(D127⋊C3) #30630715

order16002
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(D127⋊C3)
unambiguous semidirect productC3⋊(C7×D127⋊C3)

Splittings

Fitting, socleC3×C7×C127 ⋊ C2×C3
derivedC3×C127 ⋊ C2×C3×C7
HallC3×C7×C127⋊C3 ⋊ C2
HallC3×C127⋊C3 ⋊ C2×C7
HallC7×C127 ⋊ C3×D3
SylowC127 ⋊ C3×D3×C7

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(D127⋊C3)
commutator, cosocle, hypocenterC3×C127C2×C3×C7
FrattiniC1G
Fitting, socleC3×C7×C127C2×C3
LCSG ▷ C3×C127
UCSC1 ◁ C7

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

504 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C7×D127⋊C3, D7×C3⋊(D127⋊C3), (C3⋊(D127⋊C3))⋊D7, …
maximal normal subgroup ofD3×C7×D127⋊C3, D7×C3⋊(D127⋊C3), (C3⋊(D127⋊C3))⋊D7, …
maximal quotient ofC7×C3⋊((C127⋊C3)⋊C4), C2×C7×C3⋊(D127⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 72);