Finite Group Databasebeta

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C3×C5×C211⋊C3 #23748823

order9495
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C211⋊C3
unambiguous semidirect product(C5×C211)⋊C32
unambiguous semidirect product(C3×C5×C211)⋊C3

Splittings

Fitting, socleC3×C5×C211 ⋊ C3
derived, SylowC211 ⋊ C32×C5
HallC5×C211 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C5C211⋊C3
commutator, cosocle, hypocenterC211C32×C5
FrattiniC1G
Fitting, socleC3×C5×C211C3
LCSG ▷ C211
UCSC1 ◁ C3×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D211⋊C3, C3×C5⋊(D211⋊C3), C3×D5×C211⋊C3, …
maximal normal subgroup ofC3×C5×D211⋊C3, C3×C5⋊(D211⋊C3), C3×D5×C211⋊C3, …
maximal quotient ofC2×C3×C5×C211⋊C3, C5×A4×C211⋊C3, C3×C5×C22⋊(C211⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9495, 8);