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D3×D715 #22575173

order8580
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD3×D715
unambiguous semidirect product(C5×D3)⋊D143
unambiguous semidirect product(D3×C11)⋊D65
unambiguous semidirect product(D3×C13)⋊D55

Splittings

Fitting, socle, derived, HallC3×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C2×D11
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ D3×D5
HallC5×C13 ⋊ D3×D11
HallC5×C11 ⋊ D3×D13
HallC3×C13 ⋊ C2×D55
HallC3×C11 ⋊ C2×D65
HallC3×C5 ⋊ C2×D143
SylowC13 ⋊ D3×D55
SylowC11 ⋊ D3×D65
SylowC5 ⋊ D3×D143
SylowC3 ⋊ C2×D715

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C13C22
LCSG ▷ C3×C5×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1077 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD9×D715, D3×C5⋊(C11⋊(D13⋊C3)), C3×D3×D715, …
maximal normal subgroup ofD3×C5⋊(C11⋊(D13⋊C3)), C3×D3×D715
maximal quotient ofD9×D715, C3×D3×D715, D3×D2145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 145);