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C17×D17×AGL(1,𝔽7) #37566222

order24276
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×D17×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C17×D17)
unambiguous semidirect product(D7×D17)⋊(C3×C17)
unambiguous semidirect product(ΓL(1,𝔽8)×D17)⋊(C2×C17)
unambiguous semidirect product(C17×AGL(1,𝔽7))⋊(C2×C17)
unambiguous semidirect product(C17⋊AGL(1,𝔽7))⋊(C2×C17)
unambiguous semidirect product(D7×C17×D17)⋊C3

Splittings

Fitting, socle, HallC7×C172 ⋊ C22×C3
derivedC7×C17 ⋊ C22×C3×C17
HallD7×C17×D17 ⋊ C3
HallC172×ΓL(1,𝔽8) ⋊ C22
SylowC172 ⋊ C2×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×C17×D17
SylowC7 ⋊ C2×C3×C17×D17

Subgroups

subgroupG/H
center, hypercenterC17D17×AGL(1,𝔽7)
commutator, cosocle, hypocenterC7×C17C22×C3×C17
FrattiniC1G
Fitting, socleC7×C172C22×C3
LCSG ▷ C7×C17
UCSC1 ◁ C17

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 238

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 75);