Finite Group Databasebeta

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C7×D5×C13×D19 #46829154

order34580
automorphism?
homologyAbelianization (H1) = C22×C7×C13 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×C13×D19
unambiguous semidirect product(D5×C19)⋊(C2×C7×C13)
unambiguous semidirect product(C5×D19)⋊(C2×C7×C13)
unambiguous semidirect productD95⋊(C2×C7×C13)

Splittings

Fitting, socle, HallC5×C7×C13×C19 ⋊ C22
derived, HallC5×C19 ⋊ C22×C7×C13
HallC7×C13×C19 ⋊ C2×D5
HallC5×C13×C19 ⋊ C22×C7
HallC5×C7×C19 ⋊ C22×C13
HallC5×C7×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×C7×D5
HallC7×C19 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×C7×D19
HallC5×C7 ⋊ C2×C13×D19
SylowC19 ⋊ C2×C7×D5×C13
SylowC5 ⋊ C2×C7×C13×D19

Subgroups

subgroupG/H
center, hypercenterC7×C13D5×D19
commutator, cosocle, hypocenterC5×C19C22×C7×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C19C22
LCSG ▷ C5×C19
UCSC1 ◁ C7×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8645

Conjugacy classes & character table

4004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 45);