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C13⋊C3×D133 #23780592

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

Aliases

direct productC13⋊C3×D133

Splittings

Fitting, socle, derived, HallC7×C13×C19 ⋊ C2×C3
HallC7×C19×C13⋊C3 ⋊ C2
HallC13×D133 ⋊ C3
HallC19×C13⋊C3 ⋊ D7
HallC7×C13⋊C3 ⋊ D19
HallC13×C19 ⋊ C3×D7
HallC7×C19 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ C3×D19
SylowC19 ⋊ D7×C13⋊C3
SylowC13 ⋊ C3×D133
SylowC7 ⋊ D19×C13⋊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

476 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13⋊C3×D133, ((C13⋊C3)⋊D7)⋊D19, D7×D19×C13⋊C3, …
maximal normal subgroup ofD13⋊C3×D133, ((C13⋊C3)⋊D7)⋊D19, D7×D19×C13⋊C3, …
maximal quotient ofC13⋊C3×Dic133, C2×C13⋊C3×D133, C13⋊C9×D133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 83);