Finite Group Databasebeta

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C3×C17×D61⋊C5 #44527447

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

Aliases

direct productC3×C17×D61⋊C5
unambiguous semidirect product(C3×D61)⋊(C5×C17)
unambiguous semidirect product(C3×C17×D61)⋊C5

Splittings

Fitting, socle, HallC3×C17×C61 ⋊ C2×C5
derived, SylowC61 ⋊ C2×C3×C5×C17
HallC3×C17×C61⋊C5 ⋊ C2
HallC3×C17×D61 ⋊ C5
HallC17×C61⋊C5 ⋊ C2×C3
HallC17×D61 ⋊ C3×C5
HallC17×C61 ⋊ C2×C3×C5
HallC3×C61⋊C5 ⋊ C2×C17
HallC3×D61 ⋊ C5×C17
HallC61⋊C5 ⋊ C2×C3×C17
HallC3×C61 ⋊ C2×C5×C17
HallD61 ⋊ C3×C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C17D61⋊C5
commutator, cosocle, hypocenterC61C2×C3×C5×C17
FrattiniC1G
Fitting, socleC3×C17×C61C2×C5
LCSG ▷ C61
UCSC1 ◁ C3×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3111

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 20);