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ΓL(1,𝔽8)⋊C4×C289 #37566150

order24276
automorphism?
homologyAbelianization (H1) = C3×C4×C289 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C289
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C289)
unambiguous semidirect productDic7⋊(C3×C289)
unambiguous semidirect product(Dic7×C289)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C289
HallDic7×C289 ⋊ C3
HallΓL(1,𝔽8)×C289 ⋊ C4
HallC7×C289 ⋊ C3×C4
HallDic7 ⋊ C3×C289
HallΓL(1,𝔽8) ⋊ C4×C289

Subgroups

subgroupG/H
center, hypercenterC2×C289AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C289
FrattiniC2×C17C17×AGL(1,𝔽7)
FittingC2×C7×C289C2×C3
socle, cosocleC2×C7×C17C2×C3×C17
prime radicalC2×C17×ΓL(1,𝔽8)C2×C17
LCSG ▷ C7
UCSC1 ◁ C2×C289

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8092

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, 3);