Finite Group Databasebeta

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C3×C5×D1001 #44473232

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1001

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×C7×C11×C13 ⋊ C2×C3
HallC3×C7×C11×C13 ⋊ C2×C5
HallC3×C5×C11×C13 ⋊ D7
HallC3×C5×C7×C13 ⋊ D11
HallC3×C5×C7×C11 ⋊ D13
HallC5×C11×C13 ⋊ C3×D7
HallC5×C7×C13 ⋊ C3×D11
HallC3×C11×C13 ⋊ C5×D7
HallC5×C7×C11 ⋊ C3×D13
HallC3×C7×C13 ⋊ C5×D11
HallC3×C7×C11 ⋊ C5×D13
HallC3×C5×C13 ⋊ D77
HallC3×C5×C11 ⋊ D91
HallC11×C13 ⋊ C3×C5×D7
HallC3×C5×C7 ⋊ D143
HallC7×C13 ⋊ C3×C5×D11
HallC7×C11 ⋊ C3×C5×D13
HallC5×C13 ⋊ C3×D77
HallC5×C11 ⋊ C3×D91
HallC3×C13 ⋊ C5×D77
HallC5×C7 ⋊ C3×D143
HallC3×C11 ⋊ C5×D91
HallC3×C7 ⋊ C5×D143
SylowC13 ⋊ C3×C5×D77
SylowC11 ⋊ C3×C5×D91
SylowC7 ⋊ C3×C5×D143

Subgroups

subgroupG/H
center, hypercenterC3×C5D1001
commutator, cosocle, hypocenterC7×C11×C13C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C3×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

7530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 17);