Finite Group Databasebeta

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C2×C5×C19×D91 #46829191

order34580
automorphism?
homologyAbelianization (H1) = C22×C5×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C19×D91
unambiguous semidirect product(C2×C7)⋊(C5×C19×D13)
unambiguous semidirect product(C2×C13)⋊(C5×D7×C19)

Splittings

Fitting, socleC2×C5×C7×C13×C19 ⋊ C2
derived, HallC7×C13 ⋊ C22×C5×C19
HallC5×C7×C13×C19 ⋊ C22
HallC7×C13×C19 ⋊ C22×C5
HallC5×C13×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×D13
HallC5×C7×C13 ⋊ C22×C19
HallC13×C19 ⋊ C2×C5×D7
HallC7×C19 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×D7×C19
HallC5×C7 ⋊ C2×C19×D13
SylowC13 ⋊ C2×C5×D7×C19
SylowC7 ⋊ C2×C5×C19×D13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19D91
commutator, cosocle, hypocenterC7×C13C22×C5×C19
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C19C2
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17290

Conjugacy classes & character table

8930 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 82);