Finite Group Databasebeta

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C3×D5×C17×D11 #26014385

order11220
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C17×D11
unambiguous semidirect product(D5×C11)⋊(C2×C3×C17)
unambiguous semidirect product(C5×D11)⋊(C2×C3×C17)
unambiguous semidirect productD55⋊(C2×C3×C17)

Splittings

Fitting, socle, HallC3×C5×C11×C17 ⋊ C22
derived, HallC5×C11 ⋊ C22×C3×C17
HallC5×C11×C17 ⋊ C22×C3
HallC3×C11×C17 ⋊ C2×D5
HallC3×C5×C17 ⋊ C2×D11
HallC11×C17 ⋊ C2×C3×D5
HallC3×C5×C11 ⋊ C22×C17
HallC5×C17 ⋊ C2×C3×D11
HallC3×C11 ⋊ C2×D5×C17
HallC3×C5 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C3×D5×C17
SylowC5 ⋊ C2×C3×C17×D11

Subgroups

subgroupG/H
center, hypercenterC3×C17D5×D11
commutator, cosocle, hypocenterC5×C11C22×C3×C17
FrattiniC1G
Fitting, socleC3×C5×C11×C17C22
LCSG ▷ C5×C11
UCSC1 ◁ C3×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×D5×C17×D11, C32×D5×C17×D11, C3×C17×D11×D15, …
maximal normal subgroup ofC9×D5×C17×D11, C32×D5×C17×D11
maximal quotient ofC9×D5×C17×D11, C32×D5×C17×D11, C3×C17×D11×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 61);