Finite Group Databasebeta

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C23×D35⋊D11 #47978473

order35420
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×D35⋊D11
unambiguous semidirect productD35⋊(D11×C23)
unambiguous semidirect productD55⋊(D7×C23)
unambiguous semidirect productD77⋊(D5×C23)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C22
derived, HallC5×C7×C11 ⋊ C22×C23
HallC7×C11×C23 ⋊ C2×D5
HallC5×C11×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D11
HallC11×C23 ⋊ D5×D7
HallC7×C23 ⋊ D5×D11
HallC5×C23 ⋊ D7×D11
HallC7×C11 ⋊ C2×D5×C23
HallC5×C11 ⋊ C2×D7×C23
HallC5×C7 ⋊ C2×D11×C23
SylowC11 ⋊ D5×D7×C23
SylowC7 ⋊ D5×D11×C23
SylowC5 ⋊ D7×D11×C23

Subgroups

subgroupG/H
center, hypercenterC23D35⋊D11
commutator, cosocle, hypocenterC5×C7×C11C22×C23
FrattiniC1G
Fitting, socleC5×C7×C11×C23C22
LCSG ▷ C5×C7×C11
UCSC1 ◁ C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

2645 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 107);