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C5×D91⋊D19 #46829137

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

Aliases

direct productC5×D91⋊D19
unambiguous semidirect productD91⋊(C5×D19)
unambiguous semidirect productD133⋊(C5×D13)
unambiguous semidirect productD247⋊(C5×D7)

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C22
derived, HallC7×C13×C19 ⋊ C22×C5
HallC5×C13×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×C5×D7
HallC7×C19 ⋊ C2×C5×D13
HallC5×C19 ⋊ D7×D13
HallC7×C13 ⋊ C2×C5×D19
HallC5×C13 ⋊ D7×D19
HallC5×C7 ⋊ D13×D19
SylowC19 ⋊ C5×D7×D13
SylowC13 ⋊ C5×D7×D19
SylowC7 ⋊ C5×D13×D19

Subgroups

subgroupG/H
center, hypercenterC5D91⋊D19
commutator, cosocle, hypocenterC7×C13×C19C22×C5
FrattiniC1G
Fitting, socleC5×C7×C13×C19C22
LCSG ▷ C7×C13×C19
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

2315 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 28);