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C3×C7⋊(D151⋊C5) #44540259

order31710
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(D151⋊C5)
unambiguous semidirect product(C3×D1057)⋊C5

Splittings

Fitting, socle, HallC3×C7×C151 ⋊ C2×C5
derived, HallC7×C151 ⋊ C2×C3×C5
HallC3×C7×C151⋊C5 ⋊ C2
HallC3×D1057 ⋊ C5
HallC7×C151⋊C5 ⋊ C2×C3
HallC3×C151⋊C5 ⋊ D7
HallD1057 ⋊ C3×C5
HallC151⋊C5 ⋊ C3×D7
HallC3×C151 ⋊ C5×D7
SylowC151 ⋊ C3×C5×D7
HallC3×C7 ⋊ D151⋊C5
SylowC7 ⋊ C3×D151⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(D151⋊C5)
commutator, cosocle, hypocenterC7×C151C2×C3×C5
FrattiniC1G
Fitting, socleC3×C7×C151C2×C5
LCSG ▷ C7×C151
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3171

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 28);