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C5×D11×D39 #22575144

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

Aliases

direct productC5×D11×D39

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C22
derived, HallC3×C11×C13 ⋊ C22×C5
HallC5×C11×C13 ⋊ C2×D3
HallC3×C5×C13 ⋊ C2×D11
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D3
HallC5×C13 ⋊ D3×D11
HallC5×C11 ⋊ C2×D39
HallC3×C13 ⋊ C2×C5×D11
HallC3×C11 ⋊ C2×C5×D13
HallC3×C5 ⋊ D11×D13
SylowC13 ⋊ C5×D3×D11
SylowC11 ⋊ C2×C5×D39
SylowC3 ⋊ C5×D11×D13

Subgroups

subgroupG/H
center, hypercenterC5D11×D39
commutator, hypocenterC3×C11×C13C22×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C3×C11×C13
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

735 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D11×D117, C5×D11×C3⋊(D13⋊C3), C3×C5×D11×D39, …
maximal normal subgroup ofC5×D11×C3⋊(D13⋊C3), C3×C5×D11×D39
maximal quotient ofC5×D11×D117, C3×C5×D11×D39, C5×D33×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 116);