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C2×D3×C17×C11⋊C5 #26014367

order11220
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×C17×C11⋊C5
unambiguous semidirect productC3⋊(C22×C17×C11⋊C5)
unambiguous semidirect product(C2×C3)⋊(C2×C17×C11⋊C5)
unambiguous semidirect product(C2×D3×C11)⋊(C5×C17)
unambiguous semidirect product(C2×D3×C11×C17)⋊C5

Splittings

Fitting, socleC2×C3×C11×C17 ⋊ C2×C5
derived, HallC3×C11 ⋊ C22×C5×C17
HallC3×C17×C11⋊C5 ⋊ C22
HallC2×D3×C11×C17 ⋊ C5
HallC3×C11×C17 ⋊ C22×C5
HallC11×C17 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C22×C17
HallC2×D3×C11 ⋊ C5×C17
HallC3×C17 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×D3×C17
SylowC3 ⋊ C22×C17×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C17D3×C11⋊C5
commutator, cosocle, hypocenterC3×C11C22×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C11×C17C2×C5
LCSG ▷ C3×C11
UCSC1 ◁ C2×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

714 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C17×D9×C11⋊C5, D32×C17×C11⋊C5, C2×C3×D3×C17×C11⋊C5, …
maximal normal subgroup ofC2×C3×D3×C17×C11⋊C5
maximal quotient ofC2×C17×D9×C11⋊C5, D32×C17×C11⋊C5, C2×C3×D3×C17×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 43);