Finite Group Databasebeta

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C2×C3×C13⋊C3×D23 #24924540

order10764
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C13⋊C3×D23
unambiguous semidirect productC23⋊(C22×C3×C13⋊C3)
unambiguous semidirect product(C2×C23)⋊(C2×C3×C13⋊C3)
unambiguous semidirect product(C2×C13×D23)⋊C32
unambiguous semidirect product(C2×C3×C13×D23)⋊C3

Splittings

Fitting, socleC2×C3×C13×C23 ⋊ C2×C3
derived, HallC13×C23 ⋊ C22×C32
HallC3×C23×C13⋊C3 ⋊ C22
HallC2×C13×D23 ⋊ C32
SylowC23 ⋊ C22×C3×C13⋊C3
SylowC13 ⋊ C2×C32×D23

Subgroups

subgroupG/H
center, hypercenterC2×C3C13⋊C3×D23
commutator, cosocle, hypocenterC13×C23C22×C32
FrattiniC1G
Fitting, socleC2×C3×C13×C23C2×C3
LCSG ▷ C13×C23
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

546 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 76);