Finite Group Databasebeta

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C3×C23×Dic13⋊C3 #24924506

order10764
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23×Dic13⋊C3
unambiguous semidirect productDic13⋊(C32×C23)
unambiguous semidirect product(C3×Dic13)⋊(C3×C23)
unambiguous semidirect product(C23×Dic13)⋊C32
unambiguous semidirect product(C3×C23×Dic13)⋊C3

Splittings

derived, SylowC13 ⋊ C32×C4×C23
HallC3×C23×C13⋊C3 ⋊ C4
HallC23×Dic13 ⋊ C32
HallC13×C23 ⋊ C32×C4
HallC3×C13⋊C3 ⋊ C4×C23
HallDic13 ⋊ C32×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D13⋊C3
commutator, hypocenterC13C32×C4×C23
FrattiniC2C3×C23×D13⋊C3
Fitting, socleC2×C3×C13×C23C2×C3
prime radicalC2×C3×C23×C13⋊C3C2
cosocleC2×C13C2×C32×C23
LCSG ▷ C13
UCSC1 ◁ C2×C3×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 42);