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C23×C5⋊(D13⋊C3) #22582252

order8970
isoclinismisoclinic class of C5⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(C23×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D5×C23)
unambiguous semidirect productD65⋊(C3×C23)
unambiguous semidirect product(C23×D65)⋊C3

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C23
HallC5×C23×C13⋊C3 ⋊ C2
HallC23×D65 ⋊ C3
HallC23×C13⋊C3 ⋊ D5
HallC13×C23 ⋊ C3×D5
HallC5×C13⋊C3 ⋊ C2×C23
HallD65 ⋊ C3×C23
HallC5×C23 ⋊ D13⋊C3
HallC13⋊C3 ⋊ D5×C23
SylowC13 ⋊ C3×D5×C23
SylowC5 ⋊ C23×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC23C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C2×C3×C23
FrattiniC1G
Fitting, socleC5×C13×C23C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#63122⋊C3, C23⋊(#63122⋊C3), C23×#63121⋊C3, …
maximal normal subgroup ofC23×#63122⋊C3, C23⋊(#63122⋊C3), C23×#63121⋊C3, …
maximal quotient ofC23×Dic65⋊C3, C2×C23×C5⋊(D13⋊C3), C23×C5⋊(D13⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8970, 23);