Finite Group Databasebeta

← Prev (#23780568) Next (#23780570) →

ΓL(1,𝔽8)×D247 #23780569

order10374
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D247

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C3
HallC13×C19×ΓL(1,𝔽8) ⋊ C2
HallC7×D247 ⋊ C3
HallC19×ΓL(1,𝔽8) ⋊ D13
HallC13×ΓL(1,𝔽8) ⋊ D19
HallC13×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×C19 ⋊ C3×D13
HallC7×C13 ⋊ C3×D19
SylowC19 ⋊ ΓL(1,𝔽8)×D13
SylowC13 ⋊ ΓL(1,𝔽8)×D19
SylowC7 ⋊ C3×D247

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C19C2×C3
LCSG ▷ C7×C13×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

625 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D247, (ΓL(1,𝔽8)⋊D13)⋊D19, ΓL(1,𝔽8)×D13×D19, …
maximal normal subgroup ofAGL(1,𝔽7)×D247, (ΓL(1,𝔽8)⋊D13)⋊D19, ΓL(1,𝔽8)×D13×D19, …
maximal quotient ofΓL(1,𝔽8)×Dic247, C2×ΓL(1,𝔽8)×D247, C7⋊C9×D247, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 60);