Finite Group Databasebeta

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C5×D2613 #39908402

order26130
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2613
unambiguous semidirect productC3⋊(C5×D871)
unambiguous semidirect productC13⋊(C5×D201)
unambiguous semidirect productC67⋊(C5×D39)

Splittings

Fitting, socle, HallC3×C5×C13×C67 ⋊ C2
derived, HallC3×C13×C67 ⋊ C2×C5
HallC5×C13×C67 ⋊ D3
HallC3×C5×C67 ⋊ D13
HallC13×C67 ⋊ C5×D3
HallC5×C67 ⋊ D39
HallC3×C67 ⋊ C5×D13
HallC3×C5×C13 ⋊ D67
SylowC67 ⋊ C5×D39
HallC5×C13 ⋊ D201
HallC3×C13 ⋊ C5×D67
HallC3×C5 ⋊ D871
SylowC13 ⋊ C5×D201
SylowC3 ⋊ C5×D871

Subgroups

subgroupG/H
center, hypercenterC5D2613
commutator, cosocle, hypocenterC3×C13×C67C2×C5
FrattiniC1G
Fitting, socleC3×C5×C13×C67C2
LCSG ▷ C3×C13×C67
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13065

Conjugacy classes & character table

6540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26130, 16);