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Dic5×ΓL(1,𝔽8)×C71 #44447154

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

Aliases

direct productDic5×ΓL(1,𝔽8)×C71
unambiguous semidirect product(C7×Dic5)⋊(C3×C71)
unambiguous semidirect product(C7×Dic5×C71)⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C71D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C3×C4×C71
FrattiniC2D5×ΓL(1,𝔽8)×C71
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

2840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 42);