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C5×D3×D143 #22575145

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

Aliases

direct productC5×D3×D143
unambiguous semidirect product(D3×C13)⋊(C5×D11)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5D3×D143
commutator, hypocenterC3×C11×C13C22×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C3×C11×C13
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D9×D143, C5×D3×C11⋊(D13⋊C3), C3×C5×D3×D143, …
maximal normal subgroup ofC5×D3×C11⋊(D13⋊C3), C3×C5×D3×D143
maximal quotient ofC5×D9×D143, C3×C5×D3×D143, C5×D3×D429, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 117);