Finite Group Databasebeta

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C2×#16812464⋊C5 #46851902

order34770
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×#16812464⋊C5
unambiguous semidirect product(C2×#16812464)⋊C5

Splittings

Fitting, socle, HallC2×C19×C61 ⋊ C3×C5
derived, HallC19×C61 ⋊ C2×C3×C5
HallC2×C19×C61⋊C5 ⋊ C3
HallC2×#16812464 ⋊ C5
HallC19×C61⋊C5 ⋊ C2×C3
Hall#16812464 ⋊ C2×C5
HallC2×C61⋊C5 ⋊ C19⋊C3
HallC61⋊C5 ⋊ C2×C19⋊C3
HallC2×C61 ⋊ C5×C19⋊C3
SylowC61 ⋊ C2×C5×C19⋊C3
HallC2×C19 ⋊ (C61⋊C3)⋊C5
SylowC19 ⋊ C2×(C61⋊C3)⋊C5

Subgroups

subgroupG/H
center, hypercenterC2#16812464⋊C5
commutator, cosocle, hypocenterC19×C61C2×C3×C5
FrattiniC1G
Fitting, socleC2×C19×C61C3×C5
LCSG ▷ C19×C61
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2318

Conjugacy classes & character table

242 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34770, 10);