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C3⋊((Dic71⋊C5)⋊C7) #44447150

order29820
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊((Dic71⋊C5)⋊C7)
unambiguous semidirect product((C71⋊C5)⋊C7)⋊Dic3
unambiguous semidirect product(C3⋊(Dic71⋊C5))⋊C7
unambiguous semidirect product(C3⋊(Dic71⋊C7))⋊C5

Splittings

derived, HallC3×C71 ⋊ C4×C5×C7
HallC3×(C71⋊C5)⋊C7 ⋊ C4
HallC3⋊(Dic71⋊C7) ⋊ C5
HallC3⋊(Dic71⋊C5) ⋊ C7
Hall(C71⋊C5)⋊C7 ⋊ Dic3
HallC3×C71⋊C7 ⋊ C4×C5
HallC3×C71⋊C5 ⋊ C4×C7
HallDic213 ⋊ C5×C7
HallC71⋊C7 ⋊ C5×Dic3
HallC71⋊C5 ⋊ C7×Dic3
SylowC71 ⋊ C5×C7×Dic3
SylowC3 ⋊ (Dic71⋊C5)⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊AGL(1,𝔽71)
commutator, hypocenterC3×C71C4×C5×C7
Fitting, socle, cosocleC2×C3×C71C2×C5×C7
prime radicalC2×C3×(C71⋊C5)⋊C7C2
LCSG ▷ C3×C71
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 852

Polycyclic presentation:

2,3,5,7,71,2|a^2=f,b^a=b^2,e^a=e^70,e^c=e^54,e^d=e^45

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 38);