Finite Group Databasebeta

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D55⋊D161 #47978475

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

Aliases

unambiguous semidirect productD55⋊D161

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 ⋊ D5×D7
HallC7×C23 ⋊ D5×D11
HallC5×C23 ⋊ D7×D11
HallC7×C11 ⋊ D5×D23
HallC5×C11 ⋊ C2×D161
HallC5×C7 ⋊ D11×D23
SylowC23 ⋊ D35⋊D11
SylowC11 ⋊ D5×D161
SylowC7 ⋊ D55⋊D23
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

Polycyclic presentation:

2^2,5,7,11,23|d^a=d^6,e^a=e^10,f^a=f^22,c^b=c^4,e^b=e^10

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 109);