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C11⋊C5×Dic51 #26014346

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

Aliases

direct productC11⋊C5×Dic51
unambiguous semidirect productC3⋊(C11⋊C5×Dic17)
unambiguous semidirect product(C11×Dic51)⋊C5

Splittings

derived, HallC3×C11×C17 ⋊ C4×C5
HallC3×C17×C11⋊C5 ⋊ C4
HallC11×Dic51 ⋊ C5
HallC17×C11⋊C5 ⋊ Dic3
HallC11×C17 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic17
HallC3×C17 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×Dic17
SylowC17 ⋊ Dic3×C11⋊C5
SylowC11 ⋊ C5×Dic51
SylowC3 ⋊ C11⋊C5×Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D51
commutator, hypocenterC3×C11×C17C4×C5
Fitting, socle, cosocleC2×C3×C11×C17C2×C5
prime radicalC2×C3×C17×C11⋊C5C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

378 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×Dic153, C3×C11⋊C5×Dic51, C11⋊C5×C3⋊Dic51
maximal normal subgroup ofC3×C11⋊C5×Dic51
maximal quotient ofC11⋊C5×Dic153, C3×C11⋊C5×Dic51, C11⋊C5×C3⋊Dic51

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 22);