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C71×C3⋊(ΓL(1,𝔽8)⋊C4) #31822038

order17892
isoclinismisoclinic class of C3⋊AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C71 · Schur multiplier (H2) = C1

Aliases

direct productC71×C3⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC3⋊(C71×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic3×C71)
unambiguous semidirect productDic21⋊(C3×C71)
unambiguous semidirect product(C71×Dic21)⋊C3

Splittings

derivedC3×C7 ⋊ C3×C4×C71
HallC3×ΓL(1,𝔽8)×C71 ⋊ C4
HallC7×C71 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C71
SylowC7 ⋊ C3×Dic3×C71

Subgroups

subgroupG/H
center, hypercenterC2×C71C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C3×C4×C71
FrattiniC2C71×C3⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C71C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C71C2
cosocleC2×C3×C7C2×C3×C71
LCSG ▷ C3×C7
UCSC1 ◁ C2×C71

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5964

Conjugacy classes & character table

1704 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17892, 55);