Finite Group Databasebeta

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C2×C3×D23×C37⋊C3 #44499685

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

Aliases

direct productC2×C3×D23×C37⋊C3
unambiguous semidirect productC23⋊(C22×C3×C37⋊C3)
unambiguous semidirect product(C2×C23)⋊(C2×C3×C37⋊C3)
unambiguous semidirect product(C2×C37×D23)⋊C32
unambiguous semidirect product(C2×C3×C37×D23)⋊C3

Splittings

Fitting, socleC2×C3×C23×C37 ⋊ C2×C3
derived, HallC23×C37 ⋊ C22×C32
HallC3×C23×C37⋊C3 ⋊ C22
HallC2×C37×D23 ⋊ C32
SylowC37 ⋊ C2×C32×D23
SylowC23 ⋊ C22×C3×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D23×C37⋊C3
commutator, cosocle, hypocenterC23×C37C22×C32
FrattiniC1G
Fitting, socleC2×C3×C23×C37C2×C3
LCSG ▷ C23×C37
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5106

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 88);