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C3×C5×C19×ΓL(1,𝔽8)⋊C4 #37561091

order23940
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C19 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×C19×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C4×C5×C19)
unambiguous semidirect productDic7⋊(C32×C5×C19)
unambiguous semidirect product(C3×Dic7)⋊(C3×C5×C19)
unambiguous semidirect product(C5×Dic7)⋊(C32×C19)
unambiguous semidirect product(C3×C5×Dic7)⋊(C3×C19)

Splittings

derived, SylowC7 ⋊ C32×C4×C5×C19
HallC3×C5×C19×ΓL(1,𝔽8) ⋊ C4
HallC5×C19×Dic7 ⋊ C32
HallC3×C19×ΓL(1,𝔽8) ⋊ C4×C5
HallC5×C7×C19 ⋊ C32×C4
HallC19×Dic7 ⋊ C32×C5
HallC3×C5×ΓL(1,𝔽8) ⋊ C4×C19
HallC5×Dic7 ⋊ C32×C19
HallC7×C19 ⋊ C32×C4×C5
HallC3×ΓL(1,𝔽8) ⋊ C4×C5×C19
HallC5×C7 ⋊ C32×C4×C19
HallDic7 ⋊ C32×C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C19AGL(1,𝔽7)
commutator, hypocenterC7C32×C4×C5×C19
FrattiniC2C3×C5×C19×AGL(1,𝔽7)
Fitting, socleC2×C3×C5×C7×C19C2×C3
prime radicalC2×C3×C5×C19×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C32×C5×C19
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7980

Conjugacy classes & character table

3990 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 223);