Finite Group Databasebeta

← Prev (#19129780) Next (#19129782) →

D5×(C13⋊C3)⋊D7 #19129781

order5460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×(C13⋊C3)⋊D7
unambiguous semidirect product(D5×C13⋊C3)⋊D7

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C22×C3
HallD5×D91 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C22
HallC7×C13⋊C3 ⋊ C2×D5
HallC5×C13⋊C3 ⋊ C2×D7
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×C3×D7
HallC13⋊C3 ⋊ D5×D7
HallC5×C7 ⋊ C2×D13⋊C3
SylowC13 ⋊ C3×D5×D7
SylowC7 ⋊ D5×D13⋊C3
SylowC5 ⋊ C2×(C13⋊C3)⋊D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×ΓL(1,𝔽8)⋊(D13⋊C3), C3×D5×(C13⋊C3)⋊D7, D15×(C13⋊C3)⋊D7, …
maximal normal subgroup ofD5×ΓL(1,𝔽8)⋊(D13⋊C3), C3×D5×(C13⋊C3)⋊D7, C5×D5×(C13⋊C3)⋊D7, …
maximal quotient ofD5×(C13⋊C9)⋊D7, C3×D5×(C13⋊C3)⋊D7, D15×(C13⋊C3)⋊D7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 123);