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C3⋊((C23⋊C11)⋊Dic5) #29503239

order15180
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((C23⋊C11)⋊Dic5)
unambiguous semidirect product(C23⋊C11)⋊Dic15
unambiguous semidirect productDic345⋊C11

Splittings

derived, HallC3×C5×C23 ⋊ C4×C11
HallC3×C5×C23⋊C11 ⋊ C4
HallDic345 ⋊ C11
HallC5×C23⋊C11 ⋊ Dic3
HallC3×C23⋊C11 ⋊ Dic5
HallC23⋊C11 ⋊ Dic15
HallC5×C23 ⋊ C11×Dic3
HallC3×C23 ⋊ C11×Dic5
SylowC23 ⋊ C11×Dic15
HallC3×C5 ⋊ Dic23⋊C11
SylowC5 ⋊ C3⋊(Dic23⋊C11)
SylowC3 ⋊ (C23⋊C11)⋊Dic5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C5⋊AGL(1,𝔽23))
commutator, hypocenterC3×C5×C23C4×C11
Fitting, socle, cosocleC2×C3×C5×C23C2×C11
prime radicalC2×C3×C5×C23⋊C11C2
LCSG ▷ C3×C5×C23
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1380

Polycyclic presentation:

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

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 25);