Finite Group Databasebeta

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D5×D1533 #44501439

order30660
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D1533
unambiguous semidirect product(C3×D5)⋊D511
unambiguous semidirect product(C7×D5)⋊D219
unambiguous semidirect product(D5×C73)⋊D21

Splittings

Fitting, socle, derived, HallC3×C5×C7×C73 ⋊ C22
HallC5×C7×C73 ⋊ C2×D3
HallC3×C7×C73 ⋊ C2×D5
HallC3×C5×C73 ⋊ C2×D7
HallC7×C73 ⋊ D3×D5
HallC5×C73 ⋊ C2×D21
HallC3×C73 ⋊ D5×D7
HallC3×C5×C7 ⋊ C2×D73
SylowC73 ⋊ D5×D21
HallC5×C7 ⋊ C2×D219
HallC3×C7 ⋊ D5×D73
HallC3×C5 ⋊ C2×D511
SylowC7 ⋊ D5×D219
SylowC5 ⋊ C2×D1533
SylowC3 ⋊ D5×D511

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C73C22
LCSG ▷ C3×C5×C7×C73
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7665

Conjugacy classes & character table

3072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 202);