Finite Group Databasebeta

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C7×D11×D115 #47978452

order35420
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D11×D115
unambiguous semidirect product(C5×D11)⋊(C7×D23)
unambiguous semidirect product(D11×C23)⋊(C7×D5)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C22
derived, HallC5×C11×C23 ⋊ C22×C7
HallC7×C11×C23 ⋊ C2×D5
HallC5×C7×C23 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D23
HallC11×C23 ⋊ C2×C7×D5
HallC7×C23 ⋊ D5×D11
HallC5×C23 ⋊ C2×C7×D11
HallC7×C11 ⋊ C2×D115
HallC5×C11 ⋊ C2×C7×D23
HallC5×C7 ⋊ D11×D23
SylowC23 ⋊ C7×D5×D11
SylowC11 ⋊ C2×C7×D115
SylowC5 ⋊ C7×D11×D23

Subgroups

subgroupG/H
center, hypercenterC7D11×D115
commutator, cosocle, hypocenterC5×C11×C23C22×C7
FrattiniC1G
Fitting, socleC5×C7×C11×C23C22
LCSG ▷ C5×C11×C23
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

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(35420, 86);