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C3×C79×ΓL(1,𝔽8)⋊C4 #34092610

order19908
automorphism?
homologyAbelianization (H1) = C32×C4×C79 · Schur multiplier (H2) = C3

Aliases

direct productC3×C79×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C4×C79)
unambiguous semidirect productDic7⋊(C32×C79)
unambiguous semidirect product(C3×Dic7)⋊(C3×C79)

Splittings

derived, SylowC7 ⋊ C32×C4×C79
HallC3×ΓL(1,𝔽8)×C79 ⋊ C4
HallDic7×C79 ⋊ C32
HallC7×C79 ⋊ C32×C4
HallC3×ΓL(1,𝔽8) ⋊ C4×C79
HallDic7 ⋊ C32×C79

Subgroups

subgroupG/H
center, hypercenterC2×C3×C79AGL(1,𝔽7)
commutator, hypocenterC7C32×C4×C79
FrattiniC2C3×AGL(1,𝔽7)×C79
Fitting, socleC2×C3×C7×C79C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C79C2
cosocleC2×C7C2×C32×C79
LCSG ▷ C7
UCSC1 ◁ C2×C3×C79

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6636

Conjugacy classes & character table

3318 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19908, 71);