Finite Group Databasebeta

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C5×C67×D13⋊C3 #39908412

order26130
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C67 · Schur multiplier (H2) = C1

Aliases

direct productC5×C67×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×C67)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C67)
unambiguous semidirect product(C5×D13)⋊(C3×C67)

Splittings

Fitting, socle, HallC5×C13×C67 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C67
HallC5×C13⋊C3×C67 ⋊ C2
HallC5×D13×C67 ⋊ C3
HallC13⋊C3×C67 ⋊ C2×C5
HallD13×C67 ⋊ C3×C5
HallC13×C67 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C67
HallC5×D13 ⋊ C3×C67
HallC5×C13 ⋊ C2×C3×C67
HallC13⋊C3 ⋊ C2×C5×C67
HallD13 ⋊ C3×C5×C67

Subgroups

subgroupG/H
center, hypercenterC5×C67D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C67
FrattiniC1G
Fitting, socleC5×C13×C67C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C67

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4355

Conjugacy classes & character table

2680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26130, 26);