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#20293712⋊C5 #46806237

order34410
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#20293712⋊C5

Splittings

Fitting, socle, derived, HallC31×C37 ⋊ C2×C3×C5
Hall#16812215⋊C5 ⋊ C2
HallC37×D31⋊C5 ⋊ C3
Hall#20293712 ⋊ C5
HallC37×ΓL(1,𝔽32) ⋊ C2×C3
Hall#16812215 ⋊ C2×C5
HallC37×D31 ⋊ C3×C5
HallD31⋊C5 ⋊ C37⋊C3
HallΓL(1,𝔽32) ⋊ C2×C37⋊C3
HallD31 ⋊ C5×C37⋊C3
SylowC37 ⋊ AGL(1,𝔽31)
SylowC31 ⋊ C2×C5×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC31×C37C2×C3×C5
LCSG ▷ C31×C37
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1147

Polycyclic presentation:

2,3,5,31,37|d^a=d^30,d^b=d^25,e^b=e^26,d^c=d^16

Conjugacy classes & character table

187 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34410, 67);