Finite Group Databasebeta

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C5×C11×Dic87 #34062318

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

Aliases

direct productC5×C11×Dic87
unambiguous semidirect productC3⋊(C5×C11×Dic29)

Splittings

derived, HallC3×C29 ⋊ C4×C5×C11
HallC3×C5×C11×C29 ⋊ C4
HallC5×C11×C29 ⋊ Dic3
HallC3×C11×C29 ⋊ C4×C5
HallC3×C5×C29 ⋊ C4×C11
HallC11×C29 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ Dic29
HallC5×C29 ⋊ C11×Dic3
HallC3×C11 ⋊ C5×Dic29
SylowC29 ⋊ C5×C11×Dic3
HallC3×C5 ⋊ C11×Dic29
SylowC3 ⋊ C5×C11×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D87
commutator, hypocenterC3×C29C4×C5×C11
FrattiniC2C5×C11×D87
Fitting, socle, prime radicalC2×C3×C5×C11×C29C2
cosocleC2×C3×C29C2×C5×C11
LCSG ▷ C3×C29
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19140

Conjugacy classes & character table

4950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 11);