Finite Group Databasebeta

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C5×D2829 #43246609

order28290
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2829
unambiguous semidirect productC3⋊(C5×D943)
unambiguous semidirect productC23⋊(C5×D123)

Splittings

Fitting, socle, HallC3×C5×C23×C41 ⋊ C2
derived, HallC3×C23×C41 ⋊ C2×C5
HallC5×C23×C41 ⋊ D3
HallC23×C41 ⋊ C5×D3
HallC3×C5×C41 ⋊ D23
HallC3×C5×C23 ⋊ D41
HallC5×C41 ⋊ D69
HallC3×C41 ⋊ C5×D23
HallC5×C23 ⋊ D123
HallC3×C23 ⋊ C5×D41
SylowC41 ⋊ C5×D69
SylowC23 ⋊ C5×D123
HallC3×C5 ⋊ D943
SylowC3 ⋊ C5×D943

Subgroups

subgroupG/H
center, hypercenterC5D2829
commutator, cosocle, hypocenterC3×C23×C41C2×C5
FrattiniC1G
Fitting, socleC3×C5×C23×C41C2
LCSG ▷ C3×C23×C41
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14145

Conjugacy classes & character table

7080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28290, 13);