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C3⋊(C23⋊(Dic11⋊C5)) #29503246

order15180
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C23⋊(Dic11⋊C5))
unambiguous semidirect productC23⋊(C3⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊Dic69
unambiguous semidirect productDic759⋊C5

Splittings

derived, HallC3×C11×C23 ⋊ C4×C5
HallC3×C23×C11⋊C5 ⋊ C4
HallDic759 ⋊ C5
HallC23×C11⋊C5 ⋊ Dic3
HallC11×C23 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic23
HallC3×C23 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic69
HallC3×C11 ⋊ C5×Dic23
SylowC23 ⋊ C3⋊(Dic11⋊C5)
SylowC11 ⋊ C5×Dic69
SylowC3 ⋊ C23⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C23⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C23C4×C5
Fitting, socle, cosocleC2×C3×C11×C23C2×C5
prime radicalC2×C3×C23×C11⋊C5C2
LCSG ▷ C3×C11×C23
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3036

Polycyclic presentation:

2,3,5,11,23,2|a^2=f,b^a=b^2,d^a=d^10,e^a=e^22,d^c=d^4

Conjugacy classes & character table

498 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 32);