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#595×(C31⋊C3)⋊C5 #44539282

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct product#595×(C31⋊C3)⋊C5
unambiguous semidirect product(#595×C31⋊C3)⋊C5
unambiguous semidirect product(#595×ΓL(1,𝔽32))⋊C3

Splittings

Fitting, socle, derived, HallC17×C31 ⋊ C3×C4×C5
Hall#595×ΓL(1,𝔽32) ⋊ C3
HallC17×(C31⋊C3)⋊C5 ⋊ C4
Hall#595×C31⋊C3 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C3×C4
HallC31×#595 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C3×#595
HallC31⋊C3 ⋊ C5×#595
SylowC31 ⋊ C3×C5×#595
SylowC17 ⋊ C4×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC17×C31C3×C4×C5
prime radicalD17×(C31⋊C3)⋊C5C2
cosocleC31×D17C2×C3×C5
LCSG ▷ C17×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 527

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 39);