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D51×C61⋊C5 #44527452

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

Aliases

direct productD51×C61⋊C5
unambiguous semidirect productC3⋊(D17×C61⋊C5)
unambiguous semidirect productC17⋊(D3×C61⋊C5)
unambiguous semidirect product(C61×D51)⋊C5

Splittings

Fitting, socle, derived, HallC3×C17×C61 ⋊ C2×C5
HallC3×C17×C61⋊C5 ⋊ C2
HallC61×D51 ⋊ C5
HallC17×C61⋊C5 ⋊ D3
HallC17×C61 ⋊ C5×D3
HallC3×C61⋊C5 ⋊ D17
HallC3×C61 ⋊ C5×D17
SylowC61 ⋊ C5×D51
HallC3×C17 ⋊ C2×C61⋊C5
SylowC17 ⋊ D3×C61⋊C5
SylowC3 ⋊ D17×C61⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C17×C61C2×C5
LCSG ▷ C3×C17×C61
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3111

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31110, 25);