Finite Group Databasebeta

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C5×C17×D61⋊C3 #44527454

order31110
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×D61⋊C3
unambiguous semidirect product(C5×D61)⋊(C3×C17)
unambiguous semidirect product(C5×C17×D61)⋊C3

Splittings

Fitting, socle, HallC5×C17×C61 ⋊ C2×C3
derived, SylowC61 ⋊ C2×C3×C5×C17
HallC5×C17×C61⋊C3 ⋊ C2
HallC5×C17×D61 ⋊ C3
HallC17×C61⋊C3 ⋊ C2×C5
HallC17×D61 ⋊ C3×C5
HallC17×C61 ⋊ C2×C3×C5
HallC5×C61⋊C3 ⋊ C2×C17
HallC5×D61 ⋊ C3×C17
HallC5×C61 ⋊ C2×C3×C17
HallC61⋊C3 ⋊ C2×C5×C17
HallD61 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC5×C17D61⋊C3
commutator, cosocle, hypocenterC61C2×C3×C5×C17
FrattiniC1G
Fitting, socleC5×C17×C61C2×C3
LCSG ▷ C61
UCSC1 ◁ C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5185

Conjugacy classes & character table

1360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 27);