Finite Group Databasebeta

← Prev (#23780580) Next (#23780582) →

D7×#10625203 #23780581

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

Aliases

direct productD7×#10625203

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C3
HallC7×#10625203 ⋊ C2
HallC13×D7×C19 ⋊ C3
HallD7×C19 ⋊ C13⋊C3
HallC13×C19 ⋊ C3×D7
HallC13×D7 ⋊ C19⋊C3
HallC7×C19 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ C2×C19⋊C3
SylowC19 ⋊ D7×C13⋊C3
SylowC13 ⋊ D7×C19⋊C3
SylowC7 ⋊ C2×#10625203

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

425 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×#13093367, D7×#13093365, D7×#13093361, …
maximal normal subgroup ofD7×#13093367, D7×#13093365, D7×#13093361, …
maximal quotient ofDic7×#10625203, C2×D7×#10625203, D7×#14555736, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 72);