Finite Group Databasebeta

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C11⋊C5×C3⋊#595 #26014359

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

Aliases

direct productC11⋊C5×C3⋊#595
unambiguous semidirect productC3⋊(C11⋊C5×#595)
unambiguous semidirect product(C11×C3⋊#595)⋊C5

Splittings

Fitting, socle, derived, HallC3×C11×C17 ⋊ C4×C5
HallC3×C17×C11⋊C5 ⋊ C4
HallC11×C3⋊#595 ⋊ C5
HallC17×C11⋊C5 ⋊ Dic3
HallC11×C17 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ #595
HallC3×C17 ⋊ C4×C11⋊C5
HallC3×C11 ⋊ C5×#595
SylowC17 ⋊ Dic3×C11⋊C5
SylowC11 ⋊ C5×C3⋊#595
SylowC3 ⋊ C11⋊C5×#595

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C11×C17C4×C5
prime radicalC3×D17×C11⋊C5C2
cosocleC3×C11×D17C2×C5
LCSG ▷ C3×C11×C17
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×C9⋊#595, C3×C11⋊C5×C3⋊#595, C11⋊C5×C3⋊(C3⋊#595)
maximal normal subgroup ofC3×C11⋊C5×C3⋊#595
maximal quotient ofC11⋊C5×C9⋊#595, C3×C11⋊C5×C3⋊#595, C11⋊C5×C3⋊(C3⋊#595)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 35);