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C3⋊(C7⋊(Dic71⋊C5)) #44447147

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

Aliases

unambiguous semidirect productC3⋊(C7⋊(Dic71⋊C5))
unambiguous semidirect productC7⋊(C3⋊(Dic71⋊C5))
unambiguous semidirect product(C71⋊C5)⋊Dic21
unambiguous semidirect productDic1491⋊C5

Splittings

derived, HallC3×C7×C71 ⋊ C4×C5
HallC3×C7×C71⋊C5 ⋊ C4
HallDic1491 ⋊ C5
HallC7×C71⋊C5 ⋊ Dic3
HallC3×C71⋊C5 ⋊ Dic7
HallC7×C71 ⋊ C5×Dic3
HallC71⋊C5 ⋊ Dic21
HallC3×C71 ⋊ C5×Dic7
SylowC71 ⋊ C5×Dic21
HallC3×C7 ⋊ Dic71⋊C5
SylowC7 ⋊ C3⋊(Dic71⋊C5)
SylowC3 ⋊ C7⋊(Dic71⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C7⋊(D71⋊C5))
commutator, hypocenterC3×C7×C71C4×C5
Fitting, socle, cosocleC2×C3×C7×C71C2×C5
prime radicalC2×C3×C7×C71⋊C5C2
LCSG ▷ C3×C7×C71
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5964

Polycyclic presentation:

2,3,5,7,71,2|a^2=f,b^a=b^2,d^a=d^6,e^a=e^70,e^c=e^54

Conjugacy classes & character table

414 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 35);