Finite Group Databasebeta

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C3×C13⋊C3×Dic23 #24924508

order10764
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13⋊C3×Dic23
unambiguous semidirect productC23⋊(C3×C4×C13⋊C3)
unambiguous semidirect product(C13×Dic23)⋊C32
unambiguous semidirect product(C3×C13×Dic23)⋊C3

Splittings

derived, HallC13×C23 ⋊ C32×C4
HallC3×C23×C13⋊C3 ⋊ C4
HallC13×Dic23 ⋊ C32
SylowC23 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C32×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3C13⋊C3×D23
commutator, hypocenterC13×C23C32×C4
FrattiniC2C3×C13⋊C3×D23
Fitting, socleC2×C3×C13×C23C2×C3
prime radicalC2×C3×C23×C13⋊C3C2
cosocleC2×C13×C23C2×C32
LCSG ▷ C13×C23
UCSC1 ◁ C2×C3

72 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, 44);