Finite Group Databasebeta

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C5×C3⋊D231 #20294205

order6930
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊D231
unambiguous semidirect productC3⋊(C5×D231)
unambiguous semidirect productC7⋊(C5×C3⋊D33)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derived, HallC32×C7×C11 ⋊ C2×C5
HallC32×C5×C11 ⋊ D7
HallC5×C7×C11 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D11
HallC32×C11 ⋊ C5×D7
HallC7×C11 ⋊ C5×C3⋊D3
HallC32×C7 ⋊ C5×D11
HallC5×C11 ⋊ C3⋊D21
HallC32×C5 ⋊ D77
HallC5×C7 ⋊ C3⋊D33
SylowC11 ⋊ C5×C3⋊D21
SylowC32 ⋊ C5×D77
SylowC7 ⋊ C5×C3⋊D33

Subgroups

subgroupG/H
center, hypercenterC5C3⋊D231
commutator, hypocenterC32×C7×C11C2×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×C3⋊D21, C5×D7×C3⋊D33, C5×C3⋊D3×D77, …
maximal normal subgroup ofC5×D11×C3⋊D21, C5×D7×C3⋊D33, C5×C3⋊D3×D77, …
maximal quotient ofC5×C3⋊Dic231, C2×C5×C3⋊D231, C25×C3⋊D231, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 92);