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C17×D1001 #46801352

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

Aliases

direct productC17×D1001
unambiguous semidirect productC7⋊(C17×D143)
unambiguous semidirect productC11⋊(C17×D91)
unambiguous semidirect productC13⋊(C17×D77)

Splittings

Fitting, socle, HallC7×C11×C13×C17 ⋊ C2
derived, HallC7×C11×C13 ⋊ C2×C17
HallC11×C13×C17 ⋊ D7
HallC7×C13×C17 ⋊ D11
HallC7×C11×C17 ⋊ D13
HallC13×C17 ⋊ D77
HallC11×C17 ⋊ D91
HallC11×C13 ⋊ D7×C17
HallC7×C17 ⋊ D143
HallC7×C13 ⋊ C17×D11
HallC7×C11 ⋊ C17×D13
SylowC13 ⋊ C17×D77
SylowC11 ⋊ C17×D91
SylowC7 ⋊ C17×D143

Subgroups

subgroupG/H
center, hypercenterC17D1001
commutator, cosocle, hypocenterC7×C11×C13C2×C17
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

8534 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 15);