Finite Group Databasebeta

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C3×D1155 #20294201

order6930
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D1155
unambiguous semidirect productC3⋊(C3×D385)
unambiguous semidirect productC5⋊(C3×D231)
unambiguous semidirect productC11⋊(C3×D105)

Splittings

Fitting, socle, HallC32×C5×C7×C11 ⋊ C2
derivedC3×C5×C7×C11 ⋊ C2×C3
HallC32×C7×C11 ⋊ D5
HallC32×C5×C11 ⋊ D7
HallC5×C7×C11 ⋊ C3×D3
HallC32×C5×C7 ⋊ D11
HallC32×C11 ⋊ D35
HallC7×C11 ⋊ C3×D15
HallC32×C7 ⋊ D55
HallC5×C11 ⋊ C3×D21
HallC32×C5 ⋊ D77
HallC5×C7 ⋊ C3×D33
SylowC11 ⋊ C3×D105
SylowC32 ⋊ D385
SylowC7 ⋊ C3×D165
SylowC5 ⋊ C3×D231

Subgroups

subgroupG/H
center, hypercenterC3D1155
commutator, hypocenterC3×C5×C7×C11C2×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C11C2
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1737 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D11×D105, C3×D7×D165, C3×D15×D77, …
maximal normal subgroup ofC3×D11×D105, C3×D7×D165, C3×D15×D77, …
maximal quotient ofC3×Dic1155, C2×C3×D1155, C3×D5775, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 88);