Finite Group Databasebeta

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C3⋊D3×#13133722 #44501840

order30690
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3⋊D3×#13133722
unambiguous semidirect productC3⋊(D3×#13133722)

Splittings

Fitting, socle, derived, HallC32×C11×C31 ⋊ C2×C5
HallC32×#13133722 ⋊ C2
HallC11×C3⋊D3×C31 ⋊ C5
HallC3⋊D3×C31 ⋊ C11⋊C5
HallC11×C31 ⋊ C5×C3⋊D3
HallC32×C31 ⋊ C2×C11⋊C5
HallC11×C3⋊D3 ⋊ ΓL(1,𝔽32)
HallC32×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C3⋊D3×C11⋊C5
SylowC11 ⋊ C3⋊D3×ΓL(1,𝔽32)
SylowC32 ⋊ C2×#13133722

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C31C2×C5
LCSG ▷ C32×C11×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3069

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 207);