Finite Group Databasebeta

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C3×C5×D11×C59 #34085683

order19470
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C59 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D11×C59

Splittings

Fitting, socle, HallC3×C5×C11×C59 ⋊ C2
derived, SylowC11 ⋊ C2×C3×C5×C59
HallC5×C11×C59 ⋊ C2×C3
HallC3×C11×C59 ⋊ C2×C5
HallC11×C59 ⋊ C2×C3×C5
HallC3×C5×C11 ⋊ C2×C59
HallC5×C11 ⋊ C2×C3×C59
HallC3×C11 ⋊ C2×C5×C59

Subgroups

subgroupG/H
center, hypercenterC3×C5×C59D11
commutator, cosocle, hypocenterC11C2×C3×C5×C59
FrattiniC1G
Fitting, socleC3×C5×C11×C59C2
LCSG ▷ C11
UCSC1 ◁ C3×C5×C59

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9735

Conjugacy classes & character table

6195 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19470, 4);