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D11×D195 #22575160

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

Aliases

direct productD11×D195
unambiguous semidirect product(C3×D11)⋊D65
unambiguous semidirect product(C5×D11)⋊D39
unambiguous semidirect product(C13×D11)⋊D15

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 ⋊ C2×D15
HallC5×C13 ⋊ D3×D11
HallC5×C11 ⋊ C2×D39
HallC3×C13 ⋊ D5×D11
HallC3×C11 ⋊ C2×D65
HallC3×C5 ⋊ D11×D13
SylowC13 ⋊ D11×D15
SylowC11 ⋊ C2×D195
SylowC5 ⋊ D11×D39
SylowC3 ⋊ D11×D65

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

693 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×D585, D11×C3⋊(C5⋊(D13⋊C3)), C3×D11×D195, …
maximal normal subgroup ofD11×C3⋊(C5⋊(D13⋊C3)), C3×D11×D195
maximal quotient ofD11×D585, C3×D11×D195, D33⋊D195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 132);