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#16812968⋊C5 #31799007

order17670
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#16812968⋊C5

Splittings

Fitting, socle, derived, HallC19×C31 ⋊ C2×C3×C5
Hall#13183714⋊C5 ⋊ C2
HallC19×D31⋊C5 ⋊ C3
Hall#16812968 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×C3
Hall#13183714 ⋊ C2×C5
HallC19×D31 ⋊ C3×C5
HallD31⋊C5 ⋊ C19⋊C3
HallΓL(1,𝔽32) ⋊ C2×C19⋊C3
HallD31 ⋊ C5×C19⋊C3
SylowC31 ⋊ C2×C5×C19⋊C3
SylowC19 ⋊ AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC19×C31C2×C3×C5
LCSG ▷ C19×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 589

Polycyclic presentation:

2,3,5,19,31|e^a=e^30,d^b=d^7,e^b=e^5,e^c=e^16

Conjugacy classes & character table

109 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#16812968⋊C2)⋊C5, C2×#16812968⋊C5
maximal normal subgroup of(#16812968⋊C2)⋊C5, C2×#16812968⋊C5
maximal quotient of#20296612⋊C5, C2×#16812968⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 64);