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C23×C3⋊(Dic13⋊C3) #24924509

order10764
isoclinismisoclinic class of C3⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊(Dic13⋊C3)
unambiguous semidirect productC3⋊(C23×Dic13⋊C3)
unambiguous semidirect productDic39⋊(C3×C23)
unambiguous semidirect product(C23×Dic39)⋊C3

Splittings

derivedC3×C13 ⋊ C3×C4×C23
HallC3×C23×C13⋊C3 ⋊ C4
HallC13×C23 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C4×C23
SylowC13 ⋊ C3×Dic3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C3×C4×C23
FrattiniC2C23×C3⋊(D13⋊C3)
Fitting, socleC2×C3×C13×C23C2×C3
prime radicalC2×C3×C23×C13⋊C3C2
cosocleC2×C3×C13C2×C3×C23
LCSG ▷ C3×C13
UCSC1 ◁ C2×C23

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

690 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 45);