Finite Group Databasebeta

← Prev (#44540256) Next (#44540258) →

C3×C7×D151⋊C5 #44540257

order31710
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C7×C151 ⋊ C2×C5
derived, SylowC151 ⋊ C2×C3×C5×C7
HallC3×C7×C151⋊C5 ⋊ C2
HallC3×C7×D151 ⋊ C5
HallC7×C151⋊C5 ⋊ C2×C3
HallC3×C151⋊C5 ⋊ C2×C7
HallC7×D151 ⋊ C3×C5
HallC7×C151 ⋊ C2×C3×C5
HallC3×D151 ⋊ C5×C7
HallC151⋊C5 ⋊ C2×C3×C7
HallC3×C151 ⋊ C2×C5×C7
HallD151 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C7D151⋊C5
commutator, cosocle, hypocenterC151C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C151C2×C5
LCSG ▷ C151
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3171

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 26);