Finite Group Databasebeta

← Prev (#22582246) Next (#22582248) →

C5×C13⋊C3×D23 #22582247

order8970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊C3×D23
unambiguous semidirect productC23⋊(C2×C5×C13⋊C3)
unambiguous semidirect product(C13×D23)⋊(C3×C5)
unambiguous semidirect product(C5×C13×D23)⋊C3

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C2×C3
derived, HallC13×C23 ⋊ C2×C3×C5
HallC5×C23×C13⋊C3 ⋊ C2
HallC5×C13×D23 ⋊ C3
HallC23×C13⋊C3 ⋊ C2×C5
HallC13×D23 ⋊ C3×C5
HallC5×C23 ⋊ C2×C13⋊C3
HallC5×C13 ⋊ C3×D23
SylowC23 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C3×C5×D23

Subgroups

subgroupG/H
center, hypercenterC5C13⋊C3×D23
commutator, hypocenterC13×C23C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C23C2×C3
LCSG ▷ C13×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

455 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D23×D13⋊C3, D23×C5⋊(D13⋊C3), D5×C13⋊C3×D23, …
maximal normal subgroup ofC5×D23×D13⋊C3, D23×C5⋊(D13⋊C3), D5×C13⋊C3×D23, …
maximal quotient ofC5×C13⋊C3×Dic23, C2×C5×C13⋊C3×D23, C5×D23×C13⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8970, 18);