Finite Group Databasebeta

← Prev (#23780603) Next (#23780605) →

C19⋊C3×D91 #23780604

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

Aliases

direct productC19⋊C3×D91

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C3
HallC7×C13×C19⋊C3 ⋊ C2
HallC19×D91 ⋊ C3
HallC13×C19⋊C3 ⋊ D7
HallC7×C19⋊C3 ⋊ D13
HallC13×C19 ⋊ C3×D7
HallC7×C19 ⋊ C3×D13
HallC7×C13 ⋊ C2×C19⋊C3
SylowC19 ⋊ C3×D91
SylowC13 ⋊ D7×C19⋊C3
SylowC7 ⋊ D13×C19⋊C3

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

423 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×D91, ((C19⋊C3)⋊D7)⋊D13, D7×D13×C19⋊C3, …
maximal normal subgroup ofD19⋊C3×D91, ((C19⋊C3)⋊D7)⋊D13, D7×D13×C19⋊C3, …
maximal quotient ofC19⋊C3×Dic91, C2×C19⋊C3×D91, #4294×D91, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 95);