Finite Group Databasebeta

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C2×C5×#13183714 #31798949

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

Aliases

direct productC2×C5×#13183714

Splittings

Fitting, socle, HallC2×C5×C19×C31 ⋊ C3
derived, HallC19×C31 ⋊ C2×C3×C5
HallC5×C19×C31 ⋊ C2×C3
HallC2×C19×C31 ⋊ C3×C5
HallC2×C5×C31 ⋊ C19⋊C3
HallC2×C5×C19 ⋊ C31⋊C3
HallC5×C31 ⋊ C2×C19⋊C3
HallC5×C19 ⋊ C2×C31⋊C3
HallC2×C31 ⋊ C5×C19⋊C3
HallC2×C19 ⋊ C5×C31⋊C3
SylowC31 ⋊ C2×C5×C19⋊C3
SylowC19 ⋊ C2×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#13183714
commutator, cosocle, hypocenterC19×C31C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C19×C31C3
LCSG ▷ C19×C31
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5890

Conjugacy classes & character table

1990 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×#13183714, C5×#20296612, C5×#20296616, …
maximal normal subgroup ofC4×C5×#13183714, C5×#20296612, C5×#20296616, …
maximal quotient ofC4×C5×#13183714, C22×C5×#13183714

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 6);