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C7×C13×D19⋊C3 #23780539

order10374
isoclinismisoclinic class of D19⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×D19⋊C3
unambiguous semidirect productD19⋊(C3×C7×C13)
unambiguous semidirect product(C19⋊C3)⋊(C2×C7×C13)

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C7×C13
HallC7×C13×C19⋊C3 ⋊ C2
HallC7×C13×D19 ⋊ C3
HallC13×C19⋊C3 ⋊ C2×C7
HallC13×D19 ⋊ C3×C7
HallC7×C19⋊C3 ⋊ C2×C13
HallC7×D19 ⋊ C3×C13
HallC13×C19 ⋊ C2×C3×C7
HallC7×C19 ⋊ C2×C3×C13
HallC19⋊C3 ⋊ C2×C7×C13
HallD19 ⋊ C3×C7×C13

Subgroups

subgroupG/H
center, hypercenterC7×C13D19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C7×C13
FrattiniC1G
Fitting, socleC7×C13×C19C2×C3
LCSG ▷ C19
UCSC1 ◁ C7×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

819 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D13×D19⋊C3, C13×D7×D19⋊C3, D19⋊C3×D91, …
maximal normal subgroup ofC7×D13×D19⋊C3, C13×D7×D19⋊C3, D19⋊C3×D91, …
maximal quotient ofC7×C13×(C19⋊C3)⋊C4, C2×C7×C13×D19⋊C3, C7×C13×#4294⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 30);