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C29×(C5⋊D5)⋊ΓL(1,𝔽8) #44478582

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C5

Aliases

direct productC29×(C5⋊D5)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C5⋊D5)⋊(ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C29×C5⋊D5)⋊ΓL(1,𝔽8)

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derived, HallC52×C7 ⋊ C2×C3×C29
HallC29×C7⋊(C52⋊C3) ⋊ C2
HallC7×C29×C5⋊D5 ⋊ C3
HallC29×C5⋊D5 ⋊ ΓL(1,𝔽8)
HallC52×C29 ⋊ C2×ΓL(1,𝔽8)
HallC7⋊(C52⋊C3) ⋊ C2×C29
HallC7×C5⋊D5 ⋊ C3×C29
HallC7×C29 ⋊ (C5⋊D5)⋊C3
HallC5⋊D5 ⋊ ΓL(1,𝔽8)×C29
SylowC52 ⋊ C2×ΓL(1,𝔽8)×C29
SylowC7 ⋊ C29×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC29(C5⋊D5)⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC52×C7C2×C3×C29
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3045

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 66);