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((C43⋊C3)⋊C7)⋊Dic5 #31825384

order18060
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product((C43⋊C3)⋊C7)⋊Dic5
unambiguous semidirect product((C43⋊C3)⋊Dic5)⋊C7
unambiguous semidirect product((C43⋊C7)⋊Dic5)⋊C3

Splittings

derived, HallC5×C43 ⋊ C3×C4×C7
Hall(C43⋊C7)⋊Dic5 ⋊ C3
HallC5×(C43⋊C3)⋊C7 ⋊ C4
Hall(C43⋊C3)⋊Dic5 ⋊ C7
HallC5×C43⋊C7 ⋊ C3×C4
Hall(C43⋊C3)⋊C7 ⋊ Dic5
HallDic215 ⋊ C3×C7
HallC5×C43⋊C3 ⋊ C4×C7
HallC43⋊C7 ⋊ C3×Dic5
HallC43⋊C3 ⋊ C7×Dic5
SylowC43 ⋊ C3×C7×Dic5
SylowC5 ⋊ ((C43⋊C3)⋊C4)⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C5⋊AGL(1,𝔽43)
commutator, hypocenterC5×C43C3×C4×C7
Fitting, socle, cosocleC2×C5×C43C2×C3×C7
prime radicalC2×C5×(C43⋊C3)⋊C7C2
LCSG ▷ C5×C43
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 860

Polycyclic presentation:

2,3,5,7,43,2|a^2=f,c^a=c^4,e^a=e^42,e^b=e^36,e^d=e^41

Conjugacy classes & character table

178 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 60);