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C71×ΓL(1,𝔽8)⋊Dic5 #44447156

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C71 · Schur multiplier (H2) = C1

Aliases

direct productC71×ΓL(1,𝔽8)⋊Dic5
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic5×C71)
unambiguous semidirect productDic35⋊(C3×C71)
unambiguous semidirect product(C71×Dic35)⋊C3

Splittings

derived, HallC5×C7 ⋊ C3×C4×C71
HallC71×Dic35 ⋊ C3
HallC5×ΓL(1,𝔽8)×C71 ⋊ C4
HallC5×C7×C71 ⋊ C3×C4
HallΓL(1,𝔽8)×C71 ⋊ Dic5
HallC7×C71 ⋊ C3×Dic5
HallC5×C71 ⋊ ΓL(1,𝔽8)⋊C4
HallDic35 ⋊ C3×C71
HallC5×ΓL(1,𝔽8) ⋊ C4×C71
HallΓL(1,𝔽8) ⋊ Dic5×C71
SylowC7 ⋊ C3×Dic5×C71
SylowC5 ⋊ C71×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C71C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C3×C4×C71
FrattiniC2C71×C5⋊AGL(1,𝔽7)
Fitting, socleC2×C5×C7×C71C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C71C2
cosocleC2×C5×C7C2×C3×C71
LCSG ▷ C5×C7
UCSC1 ◁ C2×C71

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9940

Conjugacy classes & character table

2414 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 44);