Finite Group Databasebeta

← Prev (#35205655) Next (#35205657) →

C11×(C31⋊C3)⋊Dic5 #35205656

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

Aliases

direct productC11×(C31⋊C3)⋊Dic5
unambiguous semidirect product(C31⋊C3)⋊(C11×Dic5)
unambiguous semidirect productDic155⋊(C3×C11)
unambiguous semidirect product(C11×Dic155)⋊C3

Splittings

derived, HallC5×C31 ⋊ C3×C4×C11
HallC11×Dic155 ⋊ C3
HallC5×C11×C31⋊C3 ⋊ C4
HallC5×C11×C31 ⋊ C3×C4
HallC11×C31⋊C3 ⋊ Dic5
HallDic155 ⋊ C3×C11
HallC5×C31⋊C3 ⋊ C4×C11
HallC11×C31 ⋊ C3×Dic5
HallC31⋊C3 ⋊ C11×Dic5
HallC5×C11 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×C11×Dic5
SylowC5 ⋊ C11×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊(D31⋊C3)
commutator, hypocenterC5×C31C3×C4×C11
FrattiniC2C11×C5⋊(D31⋊C3)
Fitting, socleC2×C5×C11×C31C2×C3
prime radicalC2×C5×C11×C31⋊C3C2
cosocleC2×C5×C31C2×C3×C11
LCSG ▷ C5×C31
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 76);