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C67×D195 #39908405

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

Aliases

direct productC67×D195
unambiguous semidirect productC3⋊(C67×D65)
unambiguous semidirect productC5⋊(C67×D39)
unambiguous semidirect productC13⋊(D15×C67)

Splittings

Fitting, socle, HallC3×C5×C13×C67 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C67
HallC5×C13×C67 ⋊ D3
HallC3×C13×C67 ⋊ D5
HallC3×C5×C67 ⋊ D13
HallC13×C67 ⋊ D15
HallC5×C67 ⋊ D39
HallC3×C67 ⋊ D65
HallC5×C13 ⋊ D3×C67
HallC3×C13 ⋊ D5×C67
HallC3×C5 ⋊ D13×C67
SylowC13 ⋊ D15×C67
SylowC5 ⋊ C67×D39
SylowC3 ⋊ C67×D65

Subgroups

subgroupG/H
center, hypercenterC67D195
commutator, cosocle, hypocenterC3×C5×C13C2×C67
FrattiniC1G
Fitting, socleC3×C5×C13×C67C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C67

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13065

Conjugacy classes & character table

6633 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26130, 19);