Finite Group Databasebeta

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D23×D165 #29503306

order15180
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD23×D165
unambiguous semidirect product(C3×D23)⋊D55
unambiguous semidirect product(C5×D23)⋊D33
unambiguous semidirect product(C11×D23)⋊D15

Splittings

Fitting, socle, derived, HallC3×C5×C11×C23 ⋊ C22
HallC5×C11×C23 ⋊ C2×D3
HallC3×C11×C23 ⋊ C2×D5
HallC3×C5×C23 ⋊ C2×D11
HallC11×C23 ⋊ C2×D15
HallC3×C5×C11 ⋊ C2×D23
HallC5×C23 ⋊ C2×D33
HallC3×C23 ⋊ C2×D55
HallC5×C11 ⋊ D3×D23
HallC3×C11 ⋊ D5×D23
SylowC23 ⋊ C2×D165
HallC3×C5 ⋊ D11×D23
SylowC11 ⋊ D15×D23
SylowC5 ⋊ D23×D33
SylowC3 ⋊ D23×D55

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C23C22
LCSG ▷ C3×C5×C11×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 92);