Finite Group Databasebeta

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C3×C5×C7×C73⋊C3 #37527419

order22995
automorphism?
homologyAbelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C7×C73⋊C3
unambiguous semidirect productC73⋊(C32×C5×C7)
unambiguous semidirect product(C3×C73)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C73)⋊(C32×C7)
unambiguous semidirect product(C3×C5×C73)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C73 ⋊ C3
derived, SylowC73 ⋊ C32×C5×C7
HallC5×C7×C73 ⋊ C32
HallC7×C73 ⋊ C32×C5
HallC5×C73 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C73⋊C3
commutator, cosocle, hypocenterC73C32×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C73C3
LCSG ▷ C73
UCSC1 ◁ C3×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

2835 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22995, 11);