Finite Group Databasebeta

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C2×C5×C7×D73⋊C3 #44501363

order30660
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D73⋊C3
unambiguous semidirect productD73⋊(C2×C3×C5×C7)
unambiguous semidirect product(C73⋊C3)⋊(C22×C5×C7)
unambiguous semidirect product(C2×D73)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C73⋊C3)⋊(C2×C5×C7)
unambiguous semidirect product(C2×C5×D73)⋊(C3×C7)

Splittings

Fitting, socleC2×C5×C7×C73 ⋊ C2×C3
derived, SylowC73 ⋊ C22×C3×C5×C7
HallC2×C5×C7×D73 ⋊ C3
HallC5×C7×C73⋊C3 ⋊ C22
HallC5×C7×C73 ⋊ C22×C3
HallC2×C7×D73 ⋊ C3×C5
HallC7×C73⋊C3 ⋊ C22×C5
HallC2×C5×D73 ⋊ C3×C7
HallC5×C73⋊C3 ⋊ C22×C7
HallC7×C73 ⋊ C22×C3×C5
HallC5×C73 ⋊ C22×C3×C7
HallC2×D73 ⋊ C3×C5×C7
HallC73⋊C3 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D73⋊C3
commutator, cosocle, hypocenterC73C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C73C2×C3
LCSG ▷ C73
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5110

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 126);