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C4×C5×ΓL(1,𝔽8)×C71 #44447117

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C71 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×ΓL(1,𝔽8)×C71
unambiguous semidirect product(C4×C7)⋊(C3×C5×C71)
unambiguous semidirect product(C4×C5×C7)⋊(C3×C71)
unambiguous semidirect product(C4×C5×C7×C71)⋊C3

Splittings

Fitting, HallC4×C5×C7×C71 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C5×C71
HallC5×C7×C71 ⋊ C3×C4
HallC4×C7×C71 ⋊ C3×C5
HallC7×C71 ⋊ C3×C4×C5
HallC4×C5×C7 ⋊ C3×C71
HallC5×C7 ⋊ C3×C4×C71
HallC4×C7 ⋊ C3×C5×C71

Subgroups

subgroupG/H
center, hypercenterC4×C5×C71ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C5×C71
FrattiniC2C2×C5×ΓL(1,𝔽8)×C71
FittingC4×C5×C7×C71C3
socleC2×C5×C7×C71C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C71C2
cosocleC2×C7C2×C3×C5×C71
LCSG ▷ C7
UCSC1 ◁ C4×C5×C71

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9940

Conjugacy classes & character table

7100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 5);