Finite Group Databasebeta

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C2×C11⋊C5×D161 #47978432

order35420
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊C5×D161
unambiguous semidirect product(C2×C7)⋊(D23×C11⋊C5)
unambiguous semidirect product(C2×C23)⋊(D7×C11⋊C5)
unambiguous semidirect product(C2×C11×D161)⋊C5

Splittings

Fitting, socleC2×C7×C11×C23 ⋊ C2×C5
derived, HallC7×C11×C23 ⋊ C22×C5
HallC7×C23×C11⋊C5 ⋊ C22
HallC2×C11×D161 ⋊ C5
HallC23×C11⋊C5 ⋊ C2×D7
HallC7×C11⋊C5 ⋊ C2×D23
HallC11×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C22×C11⋊C5
HallC7×C11 ⋊ C2×C5×D23
SylowC23 ⋊ C2×D7×C11⋊C5
SylowC11 ⋊ C2×C5×D161
SylowC7 ⋊ C2×D23×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D161
commutator, cosocle, hypocenterC7×C11×C23C22×C5
FrattiniC1G
Fitting, socleC2×C7×C11×C23C2×C5
LCSG ▷ C7×C11×C23
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3542

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 66);