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C7×C17×D143 #46801344

order34034
automorphism?
homologyAbelianization (H1) = C2×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×D143
unambiguous semidirect productC11⋊(C7×C17×D13)
unambiguous semidirect productC13⋊(C7×C17×D11)

Splittings

Fitting, socle, HallC7×C11×C13×C17 ⋊ C2
derived, HallC11×C13 ⋊ C2×C7×C17
HallC11×C13×C17 ⋊ C2×C7
HallC7×C13×C17 ⋊ D11
HallC7×C11×C17 ⋊ D13
HallC7×C11×C13 ⋊ C2×C17
HallC13×C17 ⋊ C7×D11
HallC11×C17 ⋊ C7×D13
HallC7×C13 ⋊ C17×D11
HallC7×C11 ⋊ C17×D13
SylowC13 ⋊ C7×C17×D11
SylowC11 ⋊ C7×C17×D13

Subgroups

subgroupG/H
center, hypercenterC7×C17D143
commutator, cosocle, hypocenterC11×C13C2×C7×C17
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C11×C13
UCSC1 ◁ C7×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

8687 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 7);