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C4×C5×ΓL(1,𝔽8)×C79 #45684372

order33180
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C79 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×ΓL(1,𝔽8)×C79
unambiguous semidirect product(C4×C7)⋊(C3×C5×C79)
unambiguous semidirect product(C4×C5×C7)⋊(C3×C79)

Splittings

Fitting, HallC4×C5×C7×C79 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C5×C79
HallC5×C7×C79 ⋊ C3×C4
HallC4×C7×C79 ⋊ C3×C5
HallC7×C79 ⋊ C3×C4×C5
HallC4×C5×C7 ⋊ C3×C79
HallC5×C7 ⋊ C3×C4×C79
HallC4×C7 ⋊ C3×C5×C79

Subgroups

subgroupG/H
center, hypercenterC4×C5×C79ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C5×C79
FrattiniC2C2×C5×ΓL(1,𝔽8)×C79
FittingC4×C5×C7×C79C3
socleC2×C5×C7×C79C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C79C2
cosocleC2×C7C2×C3×C5×C79
LCSG ▷ C7
UCSC1 ◁ C4×C5×C79

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11060

Conjugacy classes & character table

7900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 3);