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C2×C23×C3⋊(D13⋊C3) #24924541

order10764
isoclinismisoclinic class of C3⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×C3⋊(D13⋊C3)
unambiguous semidirect product(C2×C3)⋊(C23×D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(D3×C23)
unambiguous semidirect product(C2×D39)⋊(C3×C23)
unambiguous semidirect product(C2×C23×D39)⋊C3

Splittings

Fitting, socleC2×C3×C13×C23 ⋊ C2×C3
derivedC3×C13 ⋊ C22×C3×C23
HallC3×C23×C13⋊C3 ⋊ C22
HallC13×C23 ⋊ C2×C3×D3
HallC3×C13⋊C3 ⋊ C22×C23
SylowC13 ⋊ C2×C3×D3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊(D13⋊C3)
commutator, cosocle, hypocenterC3×C13C22×C3×C23
FrattiniC1G
Fitting, socleC2×C3×C13×C23C2×C3
LCSG ▷ C3×C13
UCSC1 ◁ C2×C23

88 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, 77);