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C7×C11×D221 #46801341

order34034
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D221
unambiguous semidirect productC13⋊(C7×C11×D17)
unambiguous semidirect productC17⋊(C7×C11×D13)

Splittings

Fitting, socle, HallC7×C11×C13×C17 ⋊ C2
derived, HallC13×C17 ⋊ C2×C7×C11
HallC11×C13×C17 ⋊ C2×C7
HallC7×C13×C17 ⋊ C2×C11
HallC7×C11×C17 ⋊ D13
HallC7×C11×C13 ⋊ D17
HallC11×C17 ⋊ C7×D13
HallC11×C13 ⋊ C7×D17
HallC7×C17 ⋊ C11×D13
HallC7×C13 ⋊ C11×D17
SylowC17 ⋊ C7×C11×D13
SylowC13 ⋊ C7×C11×D17

Subgroups

subgroupG/H
center, hypercenterC7×C11D221
commutator, cosocle, hypocenterC13×C17C2×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C13×C17
UCSC1 ◁ C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

8624 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 4);