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(C11⋊C5)⋊(Dic13⋊C3) #22575064

order8580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊(Dic13⋊C3)
unambiguous semidirect product(C11⋊(Dic13⋊C3))⋊C5
unambiguous semidirect product((C11⋊C5)⋊Dic13)⋊C3

Splittings

derived, HallC11×C13 ⋊ C3×C4×C5
Hall(C11⋊C5)⋊Dic13 ⋊ C3
HallC13⋊C3×C11⋊C5 ⋊ C4
HallC11⋊(Dic13⋊C3) ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C4
HallDic143 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C4×C5
HallC11⋊C5 ⋊ Dic13⋊C3
HallC13⋊C3 ⋊ Dic11⋊C5
SylowC13 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C5×Dic13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2(C13⋊C3)⋊AGL(1,𝔽11)
commutator, hypocenterC11×C13C3×C4×C5
Fitting, socleC2×C11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

94 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×(C11⋊C5)⋊(Dic13⋊C3), C3⋊((C11⋊C5)⋊(Dic13⋊C3))
maximal normal subgroup ofC3×(C11⋊C5)⋊(Dic13⋊C3)
maximal quotient of(C11⋊C5)⋊(Dic13⋊C9), C3×(C11⋊C5)⋊(Dic13⋊C3), C3⋊((C11⋊C5)⋊(Dic13⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 36);