Finite Group Databasebeta

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C5×D3×C7×C11×C13 #44473241

order30030
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×C7×C11×C13
unambiguous semidirect productC3⋊(C2×C5×C7×C11×C13)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, SylowC3 ⋊ C2×C5×C7×C11×C13
HallC3×C7×C11×C13 ⋊ C2×C5
HallC3×C5×C11×C13 ⋊ C2×C7
HallC3×C5×C7×C13 ⋊ C2×C11
HallC3×C5×C7×C11 ⋊ C2×C13
HallC3×C11×C13 ⋊ C2×C5×C7
HallC3×C7×C13 ⋊ C2×C5×C11
HallC3×C7×C11 ⋊ C2×C5×C13
HallC3×C5×C13 ⋊ C2×C7×C11
HallC3×C5×C11 ⋊ C2×C7×C13
HallC3×C5×C7 ⋊ C2×C11×C13
HallC3×C13 ⋊ C2×C5×C7×C11
HallC3×C11 ⋊ C2×C5×C7×C13
HallC3×C7 ⋊ C2×C5×C11×C13
HallC3×C5 ⋊ C2×C7×C11×C13

Subgroups

subgroupG/H
center, hypercenterC5×C7×C11×C13D3
commutator, cosocle, hypocenterC3C2×C5×C7×C11×C13
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C3
UCSC1 ◁ C5×C7×C11×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

15015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 26);