Finite Group Databasebeta

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D11×D805 #47978458

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

Aliases

direct productD11×D805
unambiguous semidirect product(C5×D11)⋊D161
unambiguous semidirect product(C7×D11)⋊D115
unambiguous semidirect product(D11×C23)⋊D35

Splittings

Fitting, socle, derived, HallC5×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C2×D5
HallC5×C11×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D23
HallC11×C23 ⋊ C2×D35
HallC7×C23 ⋊ D5×D11
HallC5×C23 ⋊ D7×D11
HallC7×C11 ⋊ C2×D115
HallC5×C11 ⋊ C2×D161
HallC5×C7 ⋊ D11×D23
SylowC23 ⋊ D11×D35
SylowC11 ⋊ C2×D805
SylowC7 ⋊ D11×D115
SylowC5 ⋊ D11×D161

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C11×C23C22
LCSG ▷ C5×C7×C11×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

2828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 92);