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C5×C23⋊(D13⋊C3) #22582249

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

Aliases

direct productC5×C23⋊(D13⋊C3)
unambiguous semidirect productC23⋊(C5×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C5×D23)
unambiguous semidirect productD299⋊(C3×C5)
unambiguous semidirect product(C5×D299)⋊C3

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C2×C3
derived, HallC13×C23 ⋊ C2×C3×C5
HallC5×C23×C13⋊C3 ⋊ C2
HallC5×D299 ⋊ C3
HallC23×C13⋊C3 ⋊ C2×C5
HallD299 ⋊ C3×C5
HallC5×C13⋊C3 ⋊ D23
HallC5×C23 ⋊ D13⋊C3
HallC5×C13 ⋊ C3×D23
HallC13⋊C3 ⋊ C5×D23
SylowC23 ⋊ C5×D13⋊C3
SylowC13 ⋊ C3×C5×D23

Subgroups

subgroupG/H
center, hypercenterC5C23⋊(D13⋊C3)
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

425 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D23×D13⋊C3, D5×C23⋊(D13⋊C3), D115⋊(D13⋊C3), …
maximal normal subgroup ofC5×D23×D13⋊C3, D5×C23⋊(D13⋊C3), D115⋊(D13⋊C3), …
maximal quotient ofC5×C23⋊(Dic13⋊C3), C2×C5×C23⋊(D13⋊C3), C5×C23⋊(D13⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8970, 20);