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ΓL(1,𝔽8)×C29×D25 #44478545

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C29×D25
unambiguous semidirect productC25⋊(C2×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C7×D25)⋊(C3×C29)
unambiguous semidirect product(C7×C29×D25)⋊C3

Splittings

Fitting, HallC7×C25×C29 ⋊ C2×C3
derived, HallC7×C25 ⋊ C2×C3×C29
HallΓL(1,𝔽8)×C25×C29 ⋊ C2
HallC7×C29×D25 ⋊ C3
HallC25×C29 ⋊ C2×ΓL(1,𝔽8)
HallΓL(1,𝔽8)×C25 ⋊ C2×C29
HallC7×D25 ⋊ C3×C29
HallC7×C29 ⋊ C3×D25
SylowC25 ⋊ C2×ΓL(1,𝔽8)×C29
SylowC7 ⋊ C3×C29×D25

Subgroups

subgroupG/H
center, hypercenterC29ΓL(1,𝔽8)×D25
commutator, cosocle, hypocenterC7×C25C2×C3×C29
FrattiniC5D5×ΓL(1,𝔽8)×C29
FittingC7×C25×C29C2×C3
socleC5×C7×C29C3×D5
LCSG ▷ C7×C25
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

Conjugacy classes & character table

2030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 29);