Finite Group Databasebeta

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C7×C11⋊C5×C83 #44544155

order31955
automorphism?
homologyAbelianization (H1) = C5×C7×C83 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊C5×C83
unambiguous semidirect productC11⋊(C5×C7×C83)
unambiguous semidirect product(C7×C11)⋊(C5×C83)
unambiguous semidirect product(C11×C83)⋊(C5×C7)
unambiguous semidirect product(C7×C11×C83)⋊C5

Splittings

Fitting, socle, HallC7×C11×C83 ⋊ C5
derived, SylowC11 ⋊ C5×C7×C83
HallC11×C83 ⋊ C5×C7
HallC7×C11 ⋊ C5×C83

Subgroups

subgroupG/H
center, hypercenterC7×C83C11⋊C5
commutator, cosocle, hypocenterC11C5×C7×C83
FrattiniC1G
Fitting, socleC7×C11×C83C5
LCSG ▷ C11
UCSC1 ◁ C7×C83

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6391

Conjugacy classes & character table

4067 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31955, 2);