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C4×C5×ΓL(1,𝔽8)×C47 #34089449

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

Aliases

direct productC4×C5×ΓL(1,𝔽8)×C47
unambiguous semidirect product(C4×C7)⋊(C3×C5×C47)
unambiguous semidirect product(C4×C5×C7)⋊(C3×C47)
unambiguous semidirect product(C4×C7×C47)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C7×C47)⋊C3

Splittings

Fitting, HallC4×C5×C7×C47 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C5×C47
HallC5×C7×C47 ⋊ C3×C4
HallC4×C7×C47 ⋊ C3×C5
HallC7×C47 ⋊ C3×C4×C5
HallC4×C5×C7 ⋊ C3×C47
HallC5×C7 ⋊ C3×C4×C47
HallC4×C7 ⋊ C3×C5×C47

Subgroups

subgroupG/H
center, hypercenterC4×C5×C47ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C5×C47
FrattiniC2C2×C5×ΓL(1,𝔽8)×C47
FittingC4×C5×C7×C47C3
socleC2×C5×C7×C47C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C47C2
cosocleC2×C7C2×C3×C5×C47
LCSG ▷ C7
UCSC1 ◁ C4×C5×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6580

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 2);