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C5×D33⋊D17 #26014396

order11220
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D33⋊D17
unambiguous semidirect productD51⋊(C5×D11)

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C22
derived, HallC3×C11×C17 ⋊ C22×C5
HallC5×C11×C17 ⋊ C2×D3
HallC3×C5×C17 ⋊ C2×D11
HallC11×C17 ⋊ C2×C5×D3
HallC3×C5×C11 ⋊ C2×D17
HallC5×C17 ⋊ D3×D11
HallC5×C11 ⋊ D3×D17
HallC3×C17 ⋊ C2×C5×D11
HallC3×C11 ⋊ C2×C5×D17
SylowC17 ⋊ C5×D3×D11
HallC3×C5 ⋊ D11×D17
SylowC11 ⋊ C5×D3×D17
SylowC3 ⋊ C5×D11×D17

Subgroups

subgroupG/H
center, hypercenterC5D33⋊D17
commutator, cosocle, hypocenterC3×C11×C17C22×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C17C22
LCSG ▷ C3×C11×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

825 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D99⋊D17, C3×C5×D33⋊D17, C5×D51⋊D33, …
maximal normal subgroup ofC3×C5×D33⋊D17
maximal quotient ofC5×D99⋊D17, C3×C5×D33⋊D17, C5×D51⋊D33, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 72);