Finite Group Databasebeta

← Prev (#19129776) Next (#19129778) →

D5×ΓL(1,𝔽8)×D13 #19129777

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

Aliases

direct productD5×ΓL(1,𝔽8)×D13

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C22×C3
HallC7×D5×D13 ⋊ C3
HallC5×C13×ΓL(1,𝔽8) ⋊ C22
HallC13×ΓL(1,𝔽8) ⋊ C2×D5
HallC5×ΓL(1,𝔽8) ⋊ C2×D13
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C22×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D13
SylowC13 ⋊ C2×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×D5×D13
SylowC5 ⋊ C2×ΓL(1,𝔽8)×D13

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

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×ΓL(1,𝔽8)×D13⋊C3, C3×D5×ΓL(1,𝔽8)×D13, ΓL(1,𝔽8)×D13×D15, …
maximal normal subgroup ofD5×ΓL(1,𝔽8)×D13⋊C3, C3×D5×ΓL(1,𝔽8)×D13, C5×D5×ΓL(1,𝔽8)×D13, …
maximal quotient ofD5×D13×C7⋊C9, C3×D5×ΓL(1,𝔽8)×D13, ΓL(1,𝔽8)×D13×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 119);