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C7×C11⋊C5×C59 #36384249

order22715
automorphism?
homologyAbelianization (H1) = C5×C7×C59 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊C5×C59
unambiguous semidirect productC11⋊(C5×C7×C59)
unambiguous semidirect product(C7×C11)⋊(C5×C59)
unambiguous semidirect product(C11×C59)⋊(C5×C7)
unambiguous semidirect product(C7×C11×C59)⋊C5

Splittings

Fitting, socle, HallC7×C11×C59 ⋊ C5
derived, SylowC11 ⋊ C5×C7×C59
HallC11×C59 ⋊ C5×C7
HallC7×C11 ⋊ C5×C59

Subgroups

subgroupG/H
center, hypercenterC7×C59C11⋊C5
commutator, cosocle, hypocenterC11C5×C7×C59
FrattiniC1G
Fitting, socleC7×C11×C59C5
LCSG ▷ C11
UCSC1 ◁ C7×C59

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4543

Conjugacy classes & character table

2891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22715, 2);