Finite Group Databasebeta

← Prev (#22575053) Next (#22575055) →

C3⋊((C11⋊C5)⋊Dic13) #22575054

order8580
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊Dic13)
unambiguous semidirect product(C11⋊C5)⋊Dic39
unambiguous semidirect productDic429⋊C5

Splittings

derived, HallC3×C11×C13 ⋊ C4×C5
HallC3×C13×C11⋊C5 ⋊ C4
HallDic429 ⋊ C5
HallC13×C11⋊C5 ⋊ Dic3
HallC3×C11⋊C5 ⋊ Dic13
HallC11×C13 ⋊ C5×Dic3
HallC11⋊C5 ⋊ Dic39
HallC3×C13 ⋊ Dic11⋊C5
HallC3×C11 ⋊ C5×Dic13
SylowC13 ⋊ C3⋊(Dic11⋊C5)
SylowC11 ⋊ C5×Dic39
SylowC3 ⋊ (C11⋊C5)⋊Dic13

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C13⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C13C4×C5
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,11,13,2|a^2=f,b^a=b^2,d^a=d^10,e^a=e^12,d^c=d^4

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊((C11⋊C5)⋊Dic13), C3⋊((C11⋊C5)⋊(Dic13⋊C3)), C3×C3⋊((C11⋊C5)⋊Dic13), …
maximal normal subgroup ofC3⋊((C11⋊C5)⋊(Dic13⋊C3)), C3×C3⋊((C11⋊C5)⋊Dic13)
maximal quotient ofC9⋊((C11⋊C5)⋊Dic13), C3×C3⋊((C11⋊C5)⋊Dic13), C3⋊(C3⋊((C11⋊C5)⋊Dic13))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 26);