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C17×C3⋊(C17⋊AGL(1,𝔽7)) #49138802

order36414
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×C3⋊(C17⋊AGL(1,𝔽7))
unambiguous semidirect productC3⋊(C17×C17⋊AGL(1,𝔽7))
unambiguous semidirect productC17⋊(C17×C3⋊AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C17×D51)
unambiguous semidirect productD357⋊(C3×C17)
unambiguous semidirect product(C17×D357)⋊C3

Splittings

Fitting, socleC3×C7×C172 ⋊ C2×C3
derivedC3×C7×C17 ⋊ C2×C3×C17
HallC3×C172×ΓL(1,𝔽8) ⋊ C2
HallC7×C172 ⋊ C3×D3
SylowC172 ⋊ C3⋊AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C17×D17
SylowC7 ⋊ C3×C17×D51

Subgroups

subgroupG/H
center, hypercenterC17C3⋊(C17⋊AGL(1,𝔽7))
commutator, cosocle, hypocenterC3×C7×C17C2×C3×C17
FrattiniC1G
Fitting, socleC3×C7×C172C2×C3
LCSG ▷ C3×C7×C17
UCSC1 ◁ C17

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 714

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36414, 97);