Finite Group Databasebeta

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C3×C5×C11×#1181 #34062353

order19140
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×#1181

Splittings

Fitting, socle, HallC3×C5×C11×C29 ⋊ C4
derived, SylowC29 ⋊ C3×C4×C5×C11
HallC5×C11×C29 ⋊ C3×C4
HallC3×C11×C29 ⋊ C4×C5
HallC3×C5×C29 ⋊ C4×C11
HallC11×C29 ⋊ C3×C4×C5
HallC5×C29 ⋊ C3×C4×C11
HallC3×C29 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11#1181
commutator, hypocenterC29C3×C4×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C29C4
prime radicalC3×C5×C11×D29C2
cosocleD29C2×C3×C5×C11
LCSG ▷ C29
UCSC1 ◁ C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 46);