Finite Group Databasebeta

← Prev (#22575084) Next (#22575086) →

C11⋊C5×C22⋊(C13⋊C3) #22575085

order8580
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC11⋊C5×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C13⋊C3×C11⋊C5)
unambiguous semidirect productC11⋊(C5×C22⋊(C13⋊C3))
unambiguous semidirect productC13⋊(A4×C11⋊C5)
unambiguous semidirect product(C22×C11⋊C5)⋊(C13⋊C3)
unambiguous semidirect product(C13×C11⋊C5)⋊A4
unambiguous semidirect product(C11×C22⋊(C13⋊C3))⋊C5

Splittings

Fitting, socle, derived, HallC22×C11×C13 ⋊ C3×C5
HallC22×C13×C11⋊C5 ⋊ C3
HallC11×C22⋊(C13⋊C3) ⋊ C5
HallC13×C11⋊C5 ⋊ A4
HallC22×C11⋊C5 ⋊ C13⋊C3
HallC11×C13 ⋊ C5×A4
HallC22×C13 ⋊ C3×C11⋊C5
HallC22×C11 ⋊ C5×C13⋊C3
SylowC13 ⋊ A4×C11⋊C5
SylowC11 ⋊ C5×C22⋊(C13⋊C3)
SylowC22 ⋊ C13⋊C3×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC22×C11×C13C3×C5
LCSG ▷ C22×C11×C13
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×C13⋊C3×C11⋊C5, C3×C11⋊C5×C22⋊(C13⋊C3)
maximal normal subgroup ofA4×C13⋊C3×C11⋊C5, C3×C11⋊C5×C22⋊(C13⋊C3)
maximal quotient ofC11⋊C5×C22⋊(C13⋊C9), C3×C11⋊C5×C22⋊(C13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 57);