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C2×C5×C11⋊(D13⋊C3) #22575113

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

Aliases

direct productC2×C5×C11⋊(D13⋊C3)
unambiguous semidirect product(C2×C13⋊C3)⋊(C5×D11)
unambiguous semidirect product(C2×C5×D143)⋊C3

Splittings

Fitting, socleC2×C5×C11×C13 ⋊ C2×C3
derived, HallC11×C13 ⋊ C22×C3×C5
HallC2×C5×D143 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C22
HallC5×C11×C13 ⋊ C22×C3
HallC2×D143 ⋊ 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, hypercenterC2×C5C11⋊(D13⋊C3)
commutator, hypocenterC11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C11×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

430 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×C11⋊(D13⋊C3), C2×C3×C5×C11⋊(D13⋊C3), C2×C5×C3⋊(C11⋊(D13⋊C3))
maximal normal subgroup ofC2×C3×C5×C11⋊(D13⋊C3)
maximal quotient ofC2×C5×C11⋊(D13⋊C9), C5×D3×C11⋊(D13⋊C3), C2×C3×C5×C11⋊(D13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 85);