Finite Group Databasebeta

← Prev (#22575110) Next (#22575112) →

C2×C11⋊C5×D39 #22575111

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

Aliases

direct productC2×C11⋊C5×D39
unambiguous semidirect product(C2×C3)⋊(D13×C11⋊C5)
unambiguous semidirect product(C2×C13)⋊(D3×C11⋊C5)
unambiguous semidirect product(C2×C11×D39)⋊C5

Splittings

Fitting, socleC2×C3×C11×C13 ⋊ C2×C5
derived, HallC3×C11×C13 ⋊ C22×C5
HallC3×C13×C11⋊C5 ⋊ C22
HallC2×C11×D39 ⋊ C5
HallC13×C11⋊C5 ⋊ C2×D3
HallC3×C11⋊C5 ⋊ C2×D13
HallC11×C13 ⋊ C2×C5×D3
HallC3×C13 ⋊ C22×C11⋊C5
HallC3×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C2×D3×C11⋊C5
SylowC11 ⋊ C2×C5×D39
SylowC3 ⋊ C2×D13×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D39
commutator, hypocenterC3×C11×C13C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

294 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×D117, C2×C11⋊C5×C3⋊(D13⋊C3), D3×C11⋊C5×D39, …
maximal normal subgroup ofC2×C11⋊C5×C3⋊(D13⋊C3), C2×C3×C11⋊C5×D39
maximal quotient ofC2×C11⋊C5×D117, D3×C11⋊C5×D39, C2×C3×C11⋊C5×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 83);