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C2×C5⋊(C11⋊(D13⋊C3)) #22575117

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

Aliases

direct productC2×C5⋊(C11⋊(D13⋊C3))
unambiguous semidirect product(C2×C5)⋊(C11⋊(D13⋊C3))
unambiguous semidirect product(C2×C11)⋊(C5⋊(D13⋊C3))
unambiguous semidirect product(C2×C13⋊C3)⋊D55
unambiguous semidirect product(C2×D715)⋊C3

Splittings

Fitting, socleC2×C5×C11×C13 ⋊ C2×C3
derived, HallC5×C11×C13 ⋊ C22×C3
HallC2×D715 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C22
HallC11×C13⋊C3 ⋊ C2×D5
HallC5×C13⋊C3 ⋊ C2×D11
HallC11×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×C3×D11
HallC5×C11 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×D55
SylowC13 ⋊ C2×C3×D55
SylowC11 ⋊ C2×C5⋊(D13⋊C3)
SylowC5 ⋊ C2×C11⋊(D13⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C11⋊(D13⋊C3))
commutator, hypocenterC5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C5×C11×C13C2×C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

394 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 89);