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C11×C13×D119 #46801347

order34034
automorphism?
homologyAbelianization (H1) = C2×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC11×C13×D119
unambiguous semidirect productC7⋊(C11×C13×D17)
unambiguous semidirect productC17⋊(C11×C13×D7)

Splittings

Fitting, socle, HallC7×C11×C13×C17 ⋊ C2
derived, HallC7×C17 ⋊ C2×C11×C13
HallC11×C13×C17 ⋊ D7
HallC7×C13×C17 ⋊ C2×C11
HallC7×C11×C17 ⋊ C2×C13
HallC7×C11×C13 ⋊ D17
HallC13×C17 ⋊ C11×D7
HallC11×C17 ⋊ C13×D7
HallC7×C13 ⋊ C11×D17
HallC7×C11 ⋊ C13×D17
SylowC17 ⋊ C11×C13×D7
SylowC7 ⋊ C11×C13×D17

Subgroups

subgroupG/H
center, hypercenterC11×C13D119
commutator, cosocle, hypocenterC7×C17C2×C11×C13
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C7×C17
UCSC1 ◁ C11×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

8723 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 10);