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C3×C11⋊C5×Dic17 #26014342

order11220
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×Dic17
unambiguous semidirect product(C11×Dic17)⋊(C3×C5)
unambiguous semidirect product(C3×C11×Dic17)⋊C5

Splittings

derived, HallC11×C17 ⋊ C3×C4×C5
HallC3×C17×C11⋊C5 ⋊ C4
HallC3×C11×Dic17 ⋊ C5
HallC17×C11⋊C5 ⋊ C3×C4
HallC11×Dic17 ⋊ C3×C5
HallC3×C11×C17 ⋊ C4×C5
HallC3×C17 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×Dic17
SylowC17 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C3×C5×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3D17×C11⋊C5
commutator, hypocenterC11×C17C3×C4×C5
FrattiniC2C3×D17×C11⋊C5
Fitting, socleC2×C3×C11×C17C2×C5
prime radicalC2×C3×C17×C11⋊C5C2
cosocleC2×C11×C17C2×C3×C5
LCSG ▷ C11×C17
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×C11⋊C5×Dic17, C32×C11⋊C5×Dic17, C3×C11⋊C5×Dic51
maximal normal subgroup ofC9×C11⋊C5×Dic17, C32×C11⋊C5×Dic17
maximal quotient ofC9×C11⋊C5×Dic17, C32×C11⋊C5×Dic17, C3×C11⋊C5×Dic51

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 18);