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Dic5×ΓL(1,𝔽8)×C83 #46852833

order34860
automorphism?
homologyAbelianization (H1) = C3×C4×C83 · Schur multiplier (H2) = C1

Aliases

direct productDic5×ΓL(1,𝔽8)×C83
unambiguous semidirect product(C7×Dic5)⋊(C3×C83)
unambiguous semidirect product(C7×Dic5×C83)⋊C3

Splittings

derived, HallC5×C7 ⋊ C3×C4×C83
HallC7×Dic5×C83 ⋊ C3
HallC5×ΓL(1,𝔽8)×C83 ⋊ C4
HallC5×C7×C83 ⋊ C3×C4
HallC7×C83 ⋊ C3×Dic5
HallC5×C83 ⋊ C4×ΓL(1,𝔽8)
HallC7×Dic5 ⋊ C3×C83
HallC5×ΓL(1,𝔽8) ⋊ C4×C83
SylowC7 ⋊ C3×Dic5×C83
SylowC5 ⋊ C4×ΓL(1,𝔽8)×C83

Subgroups

subgroupG/H
center, hypercenterC2×C83D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C3×C4×C83
FrattiniC2D5×ΓL(1,𝔽8)×C83
Fitting, socleC2×C5×C7×C83C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C83C2
cosocleC2×C5×C7C2×C3×C83
LCSG ▷ C5×C7
UCSC1 ◁ C2×C83

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11620

Conjugacy classes & character table

3320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34860, 21);