Finite Group Databasebeta

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C5×C7×D429 #44473244

order30030
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D429
unambiguous semidirect productC3⋊(C5×C7×D143)
unambiguous semidirect productC13⋊(C5×C7×D33)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC3×C11×C13 ⋊ C2×C5×C7
HallC5×C7×C11×C13 ⋊ D3
HallC3×C7×C11×C13 ⋊ C2×C5
HallC3×C5×C11×C13 ⋊ C2×C7
HallC3×C5×C7×C13 ⋊ D11
HallC3×C5×C7×C11 ⋊ D13
HallC7×C11×C13 ⋊ C5×D3
HallC5×C11×C13 ⋊ D3×C7
HallC5×C7×C13 ⋊ D33
HallC5×C7×C11 ⋊ D39
HallC3×C7×C13 ⋊ C5×D11
HallC3×C7×C11 ⋊ C5×D13
HallC3×C5×C13 ⋊ C7×D11
HallC3×C5×C11 ⋊ C7×D13
HallC11×C13 ⋊ C5×D3×C7
HallC3×C5×C7 ⋊ D143
HallC7×C13 ⋊ C5×D33
HallC7×C11 ⋊ C5×D39
HallC5×C13 ⋊ C7×D33
HallC5×C11 ⋊ C7×D39
HallC3×C13 ⋊ C5×C7×D11
HallC3×C11 ⋊ C5×C7×D13
HallC3×C7 ⋊ C5×D143
HallC3×C5 ⋊ C7×D143
SylowC13 ⋊ C5×C7×D33
SylowC11 ⋊ C5×C7×D39
SylowC3 ⋊ C5×C7×D143

Subgroups

subgroupG/H
center, hypercenterC5×C7D429
commutator, cosocle, hypocenterC3×C11×C13C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C3×C11×C13
UCSC1 ◁ C5×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

7560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 29);