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C2×C172×AGL(1,𝔽7) #37566246

order24276
automorphism?
homologyAbelianization (H1) = C22×C3×C172 · Schur multiplier (H2) = C2×C17

Aliases

direct productC2×C172×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C2×C3×C172)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C172)
unambiguous semidirect product(C2×D7)⋊(C3×C172)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C172)
unambiguous semidirect product(C2×D7×C17)⋊(C3×C17)

Splittings

Fitting, socleC2×C7×C172 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C172
HallC2×D7×C172 ⋊ C3
HallC172×ΓL(1,𝔽8) ⋊ C22
HallC7×C172 ⋊ C22×C3
HallC2×D7 ⋊ C3×C172
HallΓL(1,𝔽8) ⋊ C22×C172

Subgroups

subgroupG/H
center, hypercenterC2×C172AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C172
FrattiniC1G
Fitting, socleC2×C7×C172C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C172

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4046

Conjugacy classes & character table

4046 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 99);