Finite Group Databasebeta

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C3⋊D3×#12045 #72254940

order4608
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C3

Aliases

direct productC3⋊D3×#12045

Splittings

FittingC32×#12045 ⋊ C2
SylowC32 ⋊ C2×#12045

Subgroups

subgroupG/H
centerC2×C4C2×D8×C3⋊D3
commutatorC32×C8C23×C8
FrattiniC4×C8C23×C3⋊D3
FittingC32×#12045C2
socleC22×C32C2×C4×D8
prime radicalC2×C3⋊D3×D16C4
cosocleC32×C4×C8C24
hypercenter#12045C3⋊D3
hypocenterC32C2×#12045
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C82 ◁ #12045

3564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1152

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊D3×#151085
maximal normal subgroup ofC3⋊D3×#151085
maximal quotient ofC3⋊D3×#151085

GAP

Past the SmallGroups library coverage — no SmallGroups id.