Finite Group Databasebeta

← Prev (#31798951) Next (#31798953) →

C2×#13183715⋊C5 #31798952

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

Aliases

direct productC2×#13183715⋊C5
unambiguous semidirect product(C2×#13183715)⋊C5

Splittings

Fitting, socle, HallC2×C19×C31 ⋊ C3×C5
derived, HallC19×C31 ⋊ C2×C3×C5
HallC2×C19×ΓL(1,𝔽32) ⋊ C3
HallC2×#13183715 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×C3
Hall#13183715 ⋊ C2×C5
HallC2×ΓL(1,𝔽32) ⋊ C19⋊C3
HallΓL(1,𝔽32) ⋊ C2×C19⋊C3
HallC2×C31 ⋊ C5×C19⋊C3
HallC2×C19 ⋊ (C31⋊C3)⋊C5
SylowC31 ⋊ C2×C5×C19⋊C3
SylowC19 ⋊ C2×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2#13183715⋊C5
commutator, cosocle, hypocenterC19×C31C2×C3×C5
FrattiniC1G
Fitting, socleC2×C19×C31C3×C5
LCSG ▷ C19×C31
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1178

Conjugacy classes & character table

166 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#13183715⋊C5, #20296611⋊C5, #20296615⋊C5, …
maximal normal subgroup ofC4×#13183715⋊C5, #20296611⋊C5, #20296615⋊C5, …
maximal quotient ofC4×#13183715⋊C5, C22×#13183715⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 9);