Finite Group Databasebeta

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D5×D1551 #44526671

order31020
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D1551
unambiguous semidirect product(C3×D5)⋊D517
unambiguous semidirect product(D5×C11)⋊D141
unambiguous semidirect product(D5×C47)⋊D33

Splittings

Fitting, socle, derived, HallC3×C5×C11×C47 ⋊ C22
HallC5×C11×C47 ⋊ C2×D3
HallC3×C11×C47 ⋊ C2×D5
HallC3×C5×C47 ⋊ C2×D11
HallC11×C47 ⋊ D3×D5
HallC5×C47 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×D47
HallC3×C47 ⋊ D5×D11
HallC5×C11 ⋊ C2×D141
SylowC47 ⋊ D5×D33
HallC3×C11 ⋊ D5×D47
HallC3×C5 ⋊ C2×D517
SylowC11 ⋊ D5×D141
SylowC5 ⋊ C2×D1551
SylowC3 ⋊ D5×D517

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C47C22
LCSG ▷ C3×C5×C11×C47
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7755

Conjugacy classes & character table

3108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31020, 74);