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C23×(C19⋊C3)⋊D13 #46801792

order34086
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×(C19⋊C3)⋊D13
unambiguous semidirect product(C19⋊C3)⋊(C23×D13)

Splittings

Fitting, socle, HallC13×C19×C23 ⋊ C2×C3
derived, HallC13×C19 ⋊ C2×C3×C23
HallC13×C23×C19⋊C3 ⋊ C2
HallC23×D247 ⋊ C3
HallC23×C19⋊C3 ⋊ D13
HallC13×C19⋊C3 ⋊ C2×C23
HallD247 ⋊ C3×C23
HallC19×C23 ⋊ C3×D13
HallC13×C23 ⋊ D19⋊C3
HallC19⋊C3 ⋊ C23×D13
SylowC19 ⋊ C3×C23×D13
SylowC13 ⋊ C23×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC23(C19⋊C3)⋊D13
commutator, cosocle, hypocenterC13×C19C2×C3×C23
FrattiniC1G
Fitting, socleC13×C19×C23C2×C3
LCSG ▷ C13×C19
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5681

Conjugacy classes & character table

1449 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34086, 41);