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C61×D255 #44527445

order31110
automorphism?
homologyAbelianization (H1) = C2×C61 · Schur multiplier (H2) = C1

Aliases

direct productC61×D255
unambiguous semidirect productC3⋊(C61×D85)
unambiguous semidirect productC5⋊(C61×D51)
unambiguous semidirect productC17⋊(D15×C61)

Splittings

Fitting, socle, HallC3×C5×C17×C61 ⋊ C2
derived, HallC3×C5×C17 ⋊ C2×C61
HallC5×C17×C61 ⋊ D3
HallC3×C17×C61 ⋊ D5
HallC17×C61 ⋊ D15
HallC3×C5×C61 ⋊ D17
HallC5×C61 ⋊ D51
HallC3×C61 ⋊ D85
HallC5×C17 ⋊ D3×C61
HallC3×C17 ⋊ D5×C61
SylowC17 ⋊ D15×C61
HallC3×C5 ⋊ D17×C61
SylowC5 ⋊ C61×D51
SylowC3 ⋊ C61×D85

Subgroups

subgroupG/H
center, hypercenterC61D255
commutator, cosocle, hypocenterC3×C5×C17C2×C61
FrattiniC1G
Fitting, socleC3×C5×C17×C61C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C61

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15555

Conjugacy classes & character table

7869 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 18);