Finite Group Databasebeta

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C7×C11×C17×D13 #46801340

order34034
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×C17×D13
unambiguous semidirect productC13⋊(C2×C7×C11×C17)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7×C11×C17D13
commutator, cosocle, hypocenterC13C2×C7×C11×C17
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C13
UCSC1 ◁ C7×C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

10472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 3);