Finite Group Databasebeta

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C3×C4×C7×C43⋊C3 #24925531

order10836
isoclinismisoclinic class of C43⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C7×C43⋊C3

Splittings

FittingC3×C4×C7×C43 ⋊ C3
derived, SylowC43 ⋊ C32×C4×C7
HallC4×C7×C43 ⋊ C32
HallC7×C43 ⋊ C32×C4
HallC4×C43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4×C7C43⋊C3
commutator, hypocenterC43C32×C4×C7
FrattiniC2C2×C3×C7×C43⋊C3
FittingC3×C4×C7×C43C3
socleC2×C3×C7×C43C2×C3
prime radicalC2×C3×C7×C43⋊C3C2
cosocleC2×C43C2×C32×C7
LCSG ▷ C43
UCSC1 ◁ C3×C4×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 123);