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C3×C23⋊(Dic13⋊C3) #24924507

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

Aliases

direct productC3×C23⋊(Dic13⋊C3)
unambiguous semidirect productC23⋊(C3×Dic13⋊C3)
unambiguous semidirect productDic299⋊C32
unambiguous semidirect product(C3×Dic299)⋊C3

Splittings

derived, HallC13×C23 ⋊ C32×C4
HallC3×C23×C13⋊C3 ⋊ C4
HallDic299 ⋊ C32
HallC3×C13⋊C3 ⋊ Dic23
SylowC23 ⋊ C3×Dic13⋊C3
SylowC13 ⋊ C32×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3C23⋊(D13⋊C3)
commutator, hypocenterC13×C23C32×C4
FrattiniC2C3×C23⋊(D13⋊C3)
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

510 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 43);