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C5×C47×ΓL(1,𝔽8)⋊C4 #34089466

order19740
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C47 · Schur multiplier (H2) = C1

Aliases

direct productC5×C47×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C5×C47)
unambiguous semidirect productDic7⋊(C3×C5×C47)
unambiguous semidirect product(C5×Dic7)⋊(C3×C47)
unambiguous semidirect product(Dic7×C47)⋊(C3×C5)
unambiguous semidirect product(C5×Dic7×C47)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C5×C47
HallC5×Dic7×C47 ⋊ C3
HallC5×ΓL(1,𝔽8)×C47 ⋊ C4
HallC5×C7×C47 ⋊ C3×C4
HallDic7×C47 ⋊ C3×C5
HallΓL(1,𝔽8)×C47 ⋊ C4×C5
HallC7×C47 ⋊ C3×C4×C5
HallC5×Dic7 ⋊ C3×C47
HallC5×ΓL(1,𝔽8) ⋊ C4×C47
HallC5×C7 ⋊ C3×C4×C47
HallDic7 ⋊ C3×C5×C47
HallΓL(1,𝔽8) ⋊ C4×C5×C47

Subgroups

subgroupG/H
center, hypercenterC2×C5×C47AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C5×C47
FrattiniC2C5×AGL(1,𝔽7)×C47
Fitting, socleC2×C5×C7×C47C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C47C2
cosocleC2×C7C2×C3×C5×C47
LCSG ▷ C7
UCSC1 ◁ C2×C5×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6580

Conjugacy classes & character table

3290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 19);