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C5×C23×D13⋊C3 #22582248

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

Aliases

direct productC5×C23×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×C23)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C23)
unambiguous semidirect product(C5×D13)⋊(C3×C23)
unambiguous semidirect product(C23×D13)⋊(C3×C5)
unambiguous semidirect product(C5×C23×D13)⋊C3

Splittings

Fitting, socle, HallC5×C13×C23 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C23
HallC5×C23×C13⋊C3 ⋊ C2
HallC5×C23×D13 ⋊ C3
HallC23×C13⋊C3 ⋊ C2×C5
HallC23×D13 ⋊ C3×C5
HallC13×C23 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C23
HallC5×D13 ⋊ C3×C23
HallC5×C13 ⋊ C2×C3×C23
HallC13⋊C3 ⋊ C2×C5×C23
HallD13 ⋊ C3×C5×C23

Subgroups

subgroupG/H
center, hypercenterC5×C23D13⋊C3
commutator, hypocenterC13C2×C3×C5×C23
FrattiniC1G
Fitting, socleC5×C13×C23C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

920 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C23×AGL(1,𝔽13), C5×C23⋊AGL(1,𝔽13), C5×D23×D13⋊C3, …
maximal normal subgroup ofC5×C23×AGL(1,𝔽13), C5×C23⋊AGL(1,𝔽13), C5×D23×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, 19);