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C3×C4×C5×ΓL(1,𝔽8)×C23 #44394452

order28980
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×C5×ΓL(1,𝔽8)×C23
unambiguous semidirect product(C4×C7)⋊(C32×C5×C23)
unambiguous semidirect product(C3×C4×C7)⋊(C3×C5×C23)
unambiguous semidirect product(C4×C5×C7)⋊(C32×C23)
unambiguous semidirect product(C3×C4×C5×C7)⋊(C3×C23)
unambiguous semidirect product(C4×C7×C23)⋊(C32×C5)
unambiguous semidirect product(C3×C4×C7×C23)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C7×C23)⋊C32
unambiguous semidirect product(C3×C4×C5×C7×C23)⋊C3

Splittings

FittingC3×C4×C5×C7×C23 ⋊ C3
derived, SylowC7 ⋊ C32×C4×C5×C23
HallC4×C5×C7×C23 ⋊ C32
HallC5×C7×C23 ⋊ C32×C4
HallC4×C7×C23 ⋊ C32×C5
HallC7×C23 ⋊ C32×C4×C5
HallC4×C5×C7 ⋊ C32×C23
HallC5×C7 ⋊ C32×C4×C23
HallC4×C7 ⋊ C32×C5×C23

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C23ΓL(1,𝔽8)
commutator, hypocenterC7C32×C4×C5×C23
FrattiniC2C2×C3×C5×ΓL(1,𝔽8)×C23
FittingC3×C4×C5×C7×C23C3
socleC2×C3×C5×C7×C23C2×C3
prime radicalC2×C3×C5×ΓL(1,𝔽8)×C23C2
cosocleC2×C7C2×C32×C5×C23
LCSG ▷ C7
UCSC1 ◁ C3×C4×C5×C23

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9660

Conjugacy classes & character table

6900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 121);