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C61×D195 #37558179

order23790
automorphism?
homologyAbelianization (H1) = C2×C61 · Schur multiplier (H2) = C1

Aliases

direct productC61×D195
unambiguous semidirect productC3⋊(C61×D65)
unambiguous semidirect productC5⋊(C61×D39)
unambiguous semidirect productC13⋊(D15×C61)

Splittings

Fitting, socle, HallC3×C5×C13×C61 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C61
HallC5×C13×C61 ⋊ D3
HallC3×C13×C61 ⋊ D5
HallC3×C5×C61 ⋊ D13
HallC13×C61 ⋊ D15
HallC5×C61 ⋊ D39
HallC3×C61 ⋊ D65
HallC5×C13 ⋊ D3×C61
HallC3×C13 ⋊ D5×C61
HallC3×C5 ⋊ D13×C61
SylowC13 ⋊ D15×C61
SylowC5 ⋊ C61×D39
SylowC3 ⋊ C61×D65

Subgroups

subgroupG/H
center, hypercenterC61D195
commutator, cosocle, hypocenterC3×C5×C13C2×C61
FrattiniC1G
Fitting, socleC3×C5×C13×C61C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C61

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11895

Conjugacy classes & character table

6039 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 24);