Finite Group Databasebeta

← Prev (#44544727) Next (#44544729) →

C3×ΓL(1,𝔽8)⋊C4×C127 #44544728

order32004
automorphism?
homologyAbelianization (H1) = C32×C4×C127 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊C4×C127
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C4×C127)
unambiguous semidirect productDic7⋊(C32×C127)
unambiguous semidirect product(C3×Dic7)⋊(C3×C127)

Splittings

derived, SylowC7 ⋊ C32×C4×C127
HallC3×ΓL(1,𝔽8)×C127 ⋊ C4
HallDic7×C127 ⋊ C32
HallC7×C127 ⋊ C32×C4
HallC3×ΓL(1,𝔽8) ⋊ C4×C127
HallDic7 ⋊ C32×C127

Subgroups

subgroupG/H
center, hypercenterC2×C3×C127AGL(1,𝔽7)
commutator, hypocenterC7C32×C4×C127
FrattiniC2C3×AGL(1,𝔽7)×C127
Fitting, socleC2×C3×C7×C127C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C127C2
cosocleC2×C7C2×C32×C127
LCSG ▷ C7
UCSC1 ◁ C2×C3×C127

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10668

Conjugacy classes & character table

5334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 110);