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C22×C13⋊C3×C11⋊C5 #22575083

order8580
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22C13⋊C3×C11⋊C5
commutator, hypocenterC11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC22×C11×C13C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C22

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4×C13⋊C3×C11⋊C5, C2×D3×C13⋊C3×C11⋊C5, C22×C3×C13⋊C3×C11⋊C5
maximal normal subgroup ofA4×C13⋊C3×C11⋊C5, C22×C3×C13⋊C3×C11⋊C5
maximal quotient ofC22×C11⋊C5×C13⋊C9, C2×D3×C13⋊C3×C11⋊C5, C22×C3×C13⋊C3×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 55);