Finite Group Databasebeta

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C3×C4×C7×C73⋊C3 #32913804

order18396
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C7×C73⋊C3
unambiguous semidirect product(C4×C73)⋊(C32×C7)
unambiguous semidirect product(C3×C4×C73)⋊(C3×C7)

Splittings

FittingC3×C4×C7×C73 ⋊ C3
derived, SylowC73 ⋊ C32×C4×C7
HallC4×C7×C73 ⋊ C32
HallC7×C73 ⋊ C32×C4
HallC4×C73 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C4×C7C73⋊C3
commutator, hypocenterC73C32×C4×C7
FrattiniC2C2×C3×C7×C73⋊C3
FittingC3×C4×C7×C73C3
socleC2×C3×C7×C73C2×C3
prime radicalC2×C3×C7×C73⋊C3C2
cosocleC2×C73C2×C32×C7
LCSG ▷ C73
UCSC1 ◁ C3×C4×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6132

Conjugacy classes & character table

2268 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18396, 122);