Finite Group Databasebeta

← Prev (#35205651) Next (#35205653) →

C5×C11×(C31⋊C3)⋊C4 #35205652

order20460
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×(C31⋊C3)⋊C4
unambiguous semidirect product(C5×Dic31)⋊(C3×C11)
unambiguous semidirect product(C5×C11×Dic31)⋊C3

Splittings

derived, SylowC31 ⋊ C3×C4×C5×C11
HallC5×C11×Dic31 ⋊ C3
HallC5×C11×C31⋊C3 ⋊ C4
HallC5×C11×C31 ⋊ C3×C4
HallC11×Dic31 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C4×C5
HallC5×Dic31 ⋊ C3×C11
HallC5×C31⋊C3 ⋊ C4×C11
HallC11×C31 ⋊ C3×C4×C5
HallC5×C31 ⋊ C3×C4×C11
HallDic31 ⋊ C3×C5×C11
HallC31⋊C3 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D31⋊C3
commutator, hypocenterC31C3×C4×C5×C11
FrattiniC2C5×C11×D31⋊C3
Fitting, socleC2×C5×C11×C31C2×C3
prime radicalC2×C5×C11×C31⋊C3C2
cosocleC2×C31C2×C3×C5×C11
LCSG ▷ C31
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6820

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 72);