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C2×C11⋊C5×D13⋊C3 #22575071

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

Aliases

direct productC2×C11⋊C5×D13⋊C3
unambiguous semidirect productD13⋊(C2×C3×C11⋊C5)
unambiguous semidirect product(C13⋊C3)⋊(C22×C11⋊C5)
unambiguous semidirect product(C2×D13)⋊(C3×C11⋊C5)
unambiguous semidirect product(C2×C13⋊C3)⋊(C2×C11⋊C5)
unambiguous semidirect product(C2×C11×D13⋊C3)⋊C5
unambiguous semidirect product(C2×D13×C11⋊C5)⋊C3

Splittings

Fitting, socleC2×C11×C13 ⋊ C2×C3×C5
derived, HallC11×C13 ⋊ C22×C3×C5
HallC2×D13×C11⋊C5 ⋊ C3
HallC13⋊C3×C11⋊C5 ⋊ C22
HallC2×C11×D13⋊C3 ⋊ C5
HallC13×C11⋊C5 ⋊ C22×C3
HallC2×C11×D13 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C22×C5
HallC2×D13 ⋊ C3×C11⋊C5
HallC13⋊C3 ⋊ C22×C11⋊C5
SylowC13 ⋊ C22×C3×C11⋊C5
SylowC11 ⋊ C2×C5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D13⋊C3
commutator, hypocenterC11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C11⋊C5×D13⋊C3, C2×C3×C11⋊C5×D13⋊C3, C2×C11⋊C5×C3⋊(D13⋊C3)
maximal normal subgroup ofC2×C3×C11⋊C5×D13⋊C3
maximal quotient ofC2×C11⋊C5×D13⋊C9, D3×C11⋊C5×D13⋊C3, C2×C3×C11⋊C5×D13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 43);