Finite Group Databasebeta

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C5×C11×Dic93 #35205603

order20460
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic93
unambiguous semidirect productC3⋊(C5×C11×Dic31)

Splittings

derived, HallC3×C31 ⋊ C4×C5×C11
HallC3×C5×C11×C31 ⋊ C4
HallC5×C11×C31 ⋊ Dic3
HallC3×C11×C31 ⋊ C4×C5
HallC3×C5×C31 ⋊ C4×C11
HallC11×C31 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ Dic31
HallC5×C31 ⋊ C11×Dic3
HallC3×C11 ⋊ C5×Dic31
SylowC31 ⋊ C5×C11×Dic3
HallC3×C5 ⋊ C11×Dic31
SylowC3 ⋊ C5×C11×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D93
commutator, hypocenterC3×C31C4×C5×C11
FrattiniC2C5×C11×D93
Fitting, socle, prime radicalC2×C3×C5×C11×C31C2
cosocleC2×C3×C31C2×C5×C11
LCSG ▷ C3×C31
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20460

Conjugacy classes & character table

5280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 23);