Finite Group Databasebeta

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C3×C7×D715 #44473236

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D715
unambiguous semidirect productC5⋊(C3×C7×D143)
unambiguous semidirect productC11⋊(C3×C7×D65)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC5×C11×C13 ⋊ C2×C3×C7
HallC5×C7×C11×C13 ⋊ C2×C3
HallC3×C7×C11×C13 ⋊ D5
HallC3×C5×C11×C13 ⋊ C2×C7
HallC3×C5×C7×C13 ⋊ D11
HallC3×C5×C7×C11 ⋊ D13
HallC7×C11×C13 ⋊ C3×D5
HallC5×C7×C13 ⋊ C3×D11
HallC3×C11×C13 ⋊ C7×D5
HallC5×C7×C11 ⋊ C3×D13
HallC3×C7×C13 ⋊ D55
HallC3×C7×C11 ⋊ D65
HallC3×C5×C13 ⋊ C7×D11
HallC3×C5×C11 ⋊ C7×D13
HallC11×C13 ⋊ C3×C7×D5
HallC3×C5×C7 ⋊ D143
HallC7×C13 ⋊ C3×D55
HallC7×C11 ⋊ C3×D65
HallC5×C13 ⋊ C3×C7×D11
HallC5×C11 ⋊ C3×C7×D13
HallC3×C13 ⋊ C7×D55
HallC5×C7 ⋊ C3×D143
HallC3×C11 ⋊ C7×D65
HallC3×C5 ⋊ C7×D143
SylowC13 ⋊ C3×C7×D55
SylowC11 ⋊ C3×C7×D65
SylowC5 ⋊ C3×C7×D143

Subgroups

subgroupG/H
center, hypercenterC3×C7D715
commutator, cosocle, hypocenterC5×C11×C13C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C5×C11×C13
UCSC1 ◁ C3×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

7539 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 21);