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C5×D11×D13⋊C3 #22575088

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D11×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×D11)
unambiguous semidirect product(C5×D11×D13)⋊C3

Splittings

Fitting, socle, HallC5×C11×C13 ⋊ C22×C3
derived, HallC11×C13 ⋊ C22×C3×C5
HallC5×D11×D13 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C22
HallD11×D13 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C22×C5
HallC5×C13⋊C3 ⋊ C2×D11
HallC5×C13 ⋊ C2×C3×D11
HallC5×C11 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×C5×D11
SylowC13 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C2×C5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D11×D13⋊C3
commutator, hypocenterC11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC5×C11×C13C22×C3
LCSG ▷ C11×C13
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×D11×D13⋊C3, C5×D33×D13⋊C3, C5×D11×C3⋊(D13⋊C3), …
maximal normal subgroup ofC3×C5×D11×D13⋊C3
maximal quotient ofC5×D11×D13⋊C9, C3×C5×D11×D13⋊C3, C5×D33×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 60);