Finite Group Databasebeta

← Prev (#22575163) Next (#22575165) →

D5×C11×D39 #22575164

order8580
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D39
unambiguous semidirect product(C3×D5)⋊(C11×D13)
unambiguous semidirect product(D5×C13)⋊(D3×C11)

Splittings

Fitting, socle, HallC3×C5×C11×C13 ⋊ C22
derived, HallC3×C5×C13 ⋊ C22×C11
HallC5×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ D3×D5
HallC5×C13 ⋊ C2×D3×C11
HallC5×C11 ⋊ C2×D39
HallC3×C13 ⋊ C2×D5×C11
HallC3×C11 ⋊ D5×D13
HallC3×C5 ⋊ C2×C11×D13
SylowC13 ⋊ D3×D5×C11
SylowC5 ⋊ C2×C11×D39
SylowC3 ⋊ D5×C11×D13

Subgroups

subgroupG/H
center, hypercenterC11D5×D39
commutator, hypocenterC3×C5×C13C22×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C22
LCSG ▷ C3×C5×C13
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

924 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C11×D117, D5×C11×C3⋊(D13⋊C3), C3×D5×C11×D39, …
maximal normal subgroup ofD5×C11×C3⋊(D13⋊C3), C3×D5×C11×D39
maximal quotient ofD5×C11×D117, C3×D5×C11×D39, C11×D15×D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 136);