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ΓL(1,𝔽8)⋊C4×C439 #49146188

order36876
automorphism?
homologyAbelianization (H1) = C3×C4×C439 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C439
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C439)
unambiguous semidirect productDic7⋊(C3×C439)

Splittings

derived, SylowC7 ⋊ C3×C4×C439
HallDic7×C439 ⋊ C3
HallΓL(1,𝔽8)×C439 ⋊ C4
HallC7×C439 ⋊ C3×C4
HallDic7 ⋊ C3×C439
HallΓL(1,𝔽8) ⋊ C4×C439

Subgroups

subgroupG/H
center, hypercenterC2×C439AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C439
FrattiniC2AGL(1,𝔽7)×C439
Fitting, socleC2×C7×C439C2×C3
prime radicalC2×ΓL(1,𝔽8)×C439C2
cosocleC2×C7C2×C3×C439
LCSG ▷ C7
UCSC1 ◁ C2×C439

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12292

Conjugacy classes & character table

6146 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36876, 18);