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D3×C13×D55 #22575171

order8580
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productD3×C13×D55
unambiguous semidirect product(C5×D3)⋊(C13×D11)
unambiguous semidirect product(D3×C11)⋊(D5×C13)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC13D3×D55
commutator, hypocenterC3×C5×C11C22×C13
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C3×C5×C11
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×D9×D55, D3×C13⋊C3×D55, C3×D3×C13×D55, …
maximal normal subgroup ofD3×C13⋊C3×D55, C3×D3×C13×D55
maximal quotient ofC13×D9×D55, C3×D3×C13×D55, D3×C13×D165, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 143);