Finite Group Databasebeta

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C3×C11×C13×D35 #44473237

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C13×D35
unambiguous semidirect productC5⋊(C3×C11×C13×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC5×C7 ⋊ C2×C3×C11×C13
HallC5×C7×C11×C13 ⋊ C2×C3
HallC3×C7×C11×C13 ⋊ D5
HallC3×C5×C11×C13 ⋊ D7
HallC3×C5×C7×C13 ⋊ C2×C11
HallC3×C5×C7×C11 ⋊ C2×C13
HallC7×C11×C13 ⋊ C3×D5
HallC5×C11×C13 ⋊ C3×D7
HallC5×C7×C13 ⋊ C2×C3×C11
HallC5×C7×C11 ⋊ C2×C3×C13
HallC3×C7×C13 ⋊ D5×C11
HallC3×C7×C11 ⋊ D5×C13
HallC3×C5×C13 ⋊ C11×D7
HallC3×C5×C11 ⋊ C13×D7
HallC3×C5×C7 ⋊ C2×C11×C13
HallC7×C13 ⋊ C3×D5×C11
HallC7×C11 ⋊ C3×D5×C13
HallC5×C13 ⋊ C3×C11×D7
HallC5×C11 ⋊ C3×C13×D7
HallC3×C7 ⋊ D5×C11×C13
HallC3×C5 ⋊ C11×C13×D7
SylowC7 ⋊ C3×D5×C11×C13
SylowC5 ⋊ C3×C11×C13×D7

Subgroups

subgroupG/H
center, hypercenterC3×C11×C13D35
commutator, cosocle, hypocenterC5×C7C2×C3×C11×C13
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C5×C7
UCSC1 ◁ C3×C11×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

8151 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 22);