Finite Group Databasebeta

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C3×Dic3×C43⋊C7 #24925498

order10836
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C43⋊C7
unambiguous semidirect productC3⋊(C3×C4×C43⋊C7)
unambiguous semidirect product(C3×Dic3×C43)⋊C7

Splittings

derivedC3×C43 ⋊ C3×C4×C7
HallC32×C43⋊C7 ⋊ C4
HallC3×Dic3×C43 ⋊ C7
HallC32×C43 ⋊ C4×C7
SylowC43 ⋊ C3×C7×Dic3
SylowC32 ⋊ C4×C43⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C3D3×C43⋊C7
commutator, hypocenterC3×C43C3×C4×C7
FrattiniC2C3×D3×C43⋊C7
Fitting, socleC2×C32×C43C2×C7
prime radicalC2×C32×C43⋊C7C2
cosocleC2×C3×C43C2×C3×C7
LCSG ▷ C3×C43
UCSC1 ◁ C2×C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 90);