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C11⋊((C31⋊C3)⋊Dic5) #35205658

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

Aliases

unambiguous semidirect productC11⋊((C31⋊C3)⋊Dic5)
unambiguous semidirect product(C31⋊C3)⋊Dic55
unambiguous semidirect productDic1705⋊C3

Splittings

derived, HallC5×C11×C31 ⋊ C3×C4
HallDic1705 ⋊ C3
HallC5×C11×C31⋊C3 ⋊ C4
HallC11×C31⋊C3 ⋊ Dic5
HallC5×C31⋊C3 ⋊ Dic11
HallC11×C31 ⋊ C3×Dic5
HallC5×C31 ⋊ C3×Dic11
HallC31⋊C3 ⋊ Dic55
HallC5×C11 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×Dic55
SylowC11 ⋊ (C31⋊C3)⋊Dic5
SylowC5 ⋊ C11⋊((C31⋊C3)⋊C4)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C5⋊(C11⋊(D31⋊C3))
commutator, hypocenterC5×C11×C31C3×C4
Fitting, socle, cosocleC2×C5×C11×C31C2×C3
prime radicalC2×C5×C11×C31⋊C3C2
LCSG ▷ C5×C11×C31
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6820

Polycyclic presentation:

2,3,5,11,31,2|a^2=f,c^a=c^4,d^a=d^10,e^a=e^30,e^b=e^25

Conjugacy classes & character table

724 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 78);