Finite Group Databasebeta

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C7×C11×C13×D17 #46801339

order34034
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×C13×D17
unambiguous semidirect productC17⋊(C2×C7×C11×C13)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7×C11×C13D17
commutator, cosocle, hypocenterC17C2×C7×C11×C13
FrattiniC1G
Fitting, socleC7×C11×C13×C17C2
LCSG ▷ C17
UCSC1 ◁ C7×C11×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17017

Conjugacy classes & character table

10010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34034, 2);