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D5×C11⋊(D13⋊C3) #22575102

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

Aliases

direct productD5×C11⋊(D13⋊C3)
unambiguous semidirect product(D5×C11)⋊(D13⋊C3)
unambiguous semidirect product(D5×C13⋊C3)⋊D11
unambiguous semidirect product(D5×D143)⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C13 ⋊ C22×C3
HallD5×D143 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C22
HallC11×C13⋊C3 ⋊ C2×D5
HallC5×C13⋊C3 ⋊ C2×D11
HallC11×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×C3×D11
HallC5×C11 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ D5×D11
SylowC13 ⋊ C3×D5×D11
SylowC11 ⋊ D5×D13⋊C3
SylowC5 ⋊ C2×C11⋊(D13⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C13C22×C3
LCSG ▷ C5×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

172 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×C11⋊(D13⋊C3), D15×C11⋊(D13⋊C3), D5×C3⋊(C11⋊(D13⋊C3)), …
maximal normal subgroup ofC3×D5×C11⋊(D13⋊C3)
maximal quotient ofD5×C11⋊(D13⋊C9), C3×D5×C11⋊(D13⋊C3), D15×C11⋊(D13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 74);