Finite Group Databasebeta

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D3×D7×C61⋊C5 #38785035

order25620
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×D7×C61⋊C5
unambiguous semidirect product(D3×C7)⋊(C2×C61⋊C5)
unambiguous semidirect product(C3×D7)⋊(C2×C61⋊C5)
unambiguous semidirect productD21⋊(C2×C61⋊C5)
unambiguous semidirect product(D3×D7×C61)⋊C5

Splittings

Fitting, socle, derived, HallC3×C7×C61 ⋊ C22×C5
HallC3×C7×C61⋊C5 ⋊ C22
HallD3×D7×C61 ⋊ C5
HallC7×C61⋊C5 ⋊ C2×D3
HallC3×C61⋊C5 ⋊ C2×D7
HallC7×C61 ⋊ C2×C5×D3
HallC3×C61 ⋊ C2×C5×D7
SylowC61 ⋊ C5×D3×D7
HallC3×C7 ⋊ C22×C61⋊C5
SylowC7 ⋊ C2×D3×C61⋊C5
SylowC3 ⋊ C2×D7×C61⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C61C22×C5
LCSG ▷ C3×C7×C61
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1281

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25620, 108);