Finite Group Databasebeta

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C3×D23×D37⋊C3 #44499671

order30636
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×D23×D37⋊C3
unambiguous semidirect productD37⋊(C32×D23)
unambiguous semidirect product(D23×D37)⋊C32
unambiguous semidirect product(C23×D37⋊C3)⋊(C2×C3)
unambiguous semidirect product(D23×C37⋊C3)⋊(C2×C3)
unambiguous semidirect product(C23⋊(D37⋊C3))⋊(C2×C3)
unambiguous semidirect product(C3×D23×D37)⋊C3

Splittings

Fitting, socleC3×C23×C37 ⋊ C22×C3
derived, HallC23×C37 ⋊ C22×C32
HallC3×C23×C37⋊C3 ⋊ C22
HallD23×D37 ⋊ C32
HallC3×C37⋊C3 ⋊ C2×D23
SylowC37 ⋊ C2×C32×D23
SylowC23 ⋊ C2×C3×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3D23×D37⋊C3
commutator, cosocle, hypocenterC23×C37C22×C32
FrattiniC1G
Fitting, socleC3×C23×C37C22×C3
LCSG ▷ C23×C37
UCSC1 ◁ C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2553

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 74);