Finite Group Databasebeta

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D3×D13×C11⋊C5 #22575082

order8580
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×D13×C11⋊C5
unambiguous semidirect product(D3×C13)⋊(C2×C11⋊C5)
unambiguous semidirect product(C3×D13)⋊(C2×C11⋊C5)
unambiguous semidirect productD39⋊(C2×C11⋊C5)
unambiguous semidirect product(D3×C11×D13)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C13 ⋊ C22×C5
HallC3×C13×C11⋊C5 ⋊ C22
HallD3×C11×D13 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×D3
HallC3×C11⋊C5 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D3
HallC3×C13 ⋊ C22×C11⋊C5
HallC3×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C2×D3×C11⋊C5
SylowC11 ⋊ C5×D3×D13
SylowC3 ⋊ C2×D13×C11⋊C5

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×D13×C11⋊C5, D3×C11⋊C5×D13⋊C3, C3×D3×D13×C11⋊C5, …
maximal normal subgroup ofD3×C11⋊C5×D13⋊C3, C3×D3×D13×C11⋊C5
maximal quotient ofD9×D13×C11⋊C5, C3×D3×D13×C11⋊C5, D3×C11⋊C5×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 54);