Finite Group Databasebeta

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D21×C151⋊C5 #44540262

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

Aliases

direct productD21×C151⋊C5
unambiguous semidirect productC3⋊(D7×C151⋊C5)
unambiguous semidirect productC7⋊(D3×C151⋊C5)
unambiguous semidirect product(D21×C151)⋊C5

Splittings

Fitting, socle, derived, HallC3×C7×C151 ⋊ C2×C5
HallC3×C7×C151⋊C5 ⋊ C2
HallD21×C151 ⋊ C5
HallC7×C151⋊C5 ⋊ D3
HallC3×C151⋊C5 ⋊ D7
HallC7×C151 ⋊ C5×D3
HallC3×C151 ⋊ C5×D7
SylowC151 ⋊ C5×D21
HallC3×C7 ⋊ C2×C151⋊C5
SylowC7 ⋊ D3×C151⋊C5
SylowC3 ⋊ D7×C151⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C151C2×C5
LCSG ▷ C3×C7×C151
UCSC1

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, 31);