Finite Group Databasebeta

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C3×A4×C13×C23 #24924581

order10764
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C13×C23 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×A4×C13×C23
unambiguous semidirect productC22⋊(C32×C13×C23)
unambiguous semidirect product(C22×C3)⋊(C3×C13×C23)
unambiguous semidirect product(C22×C23)⋊(C32×C13)
unambiguous semidirect product(C22×C3×C23)⋊(C3×C13)

Splittings

Fitting, socleC22×C3×C13×C23 ⋊ C3
derived, SylowC22 ⋊ C32×C13×C23
HallC22×C13×C23 ⋊ C32
HallC22×C23 ⋊ C32×C13
HallC22×C13 ⋊ C32×C23

Subgroups

subgroupG/H
center, hypercenterC3×C13×C23A4
commutator, cosocle, hypocenterC22C32×C13×C23
FrattiniC1G
Fitting, socleC22×C3×C13×C23C3
LCSG ▷ C22
UCSC1 ◁ C3×C13×C23

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 117);