Finite Group Databasebeta

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C7×C3⋊(D151⋊C5) #44540261

order31710
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(D151⋊C5)
unambiguous semidirect productC3⋊(C7×D151⋊C5)
unambiguous semidirect product(C151⋊C5)⋊(D3×C7)
unambiguous semidirect productD453⋊(C5×C7)
unambiguous semidirect product(C7×D453)⋊C5

Splittings

Fitting, socle, HallC3×C7×C151 ⋊ C2×C5
derived, HallC3×C151 ⋊ C2×C5×C7
HallC3×C7×C151⋊C5 ⋊ C2
HallC7×D453 ⋊ C5
HallC7×C151⋊C5 ⋊ D3
HallC3×C151⋊C5 ⋊ C2×C7
HallC7×C151 ⋊ C5×D3
HallD453 ⋊ C5×C7
HallC151⋊C5 ⋊ D3×C7
SylowC151 ⋊ C5×D3×C7
HallC3×C7 ⋊ D151⋊C5
SylowC3 ⋊ C7×D151⋊C5

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(D151⋊C5)
commutator, cosocle, hypocenterC3×C151C2×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C151C2×C5
LCSG ▷ C3×C151
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3171

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 30);