Finite Group Databasebeta

← Prev (#44478582) Next (#44478584) →

C29⋊((C5⋊D5)⋊ΓL(1,𝔽8)) #44478583

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

Aliases

unambiguous semidirect productC29⋊((C5⋊D5)⋊ΓL(1,𝔽8))
unambiguous semidirect product(C5⋊D145)⋊ΓL(1,𝔽8)

Splittings

Fitting, socle, derived, HallC52×C7×C29 ⋊ C2×C3
HallC29×C7⋊(C52⋊C3) ⋊ C2
HallC7×C5⋊D145 ⋊ C3
HallC5⋊D145 ⋊ ΓL(1,𝔽8)
HallC52×C29 ⋊ C2×ΓL(1,𝔽8)
HallC7⋊(C52⋊C3) ⋊ D29
HallC7×C29 ⋊ (C5⋊D5)⋊C3
HallC52×C7 ⋊ C3×D29
SylowC29 ⋊ (C5⋊D5)⋊ΓL(1,𝔽8)
SylowC52 ⋊ ΓL(1,𝔽8)×D29
SylowC7 ⋊ C29⋊((C5⋊D5)⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C29C2×C3
LCSG ▷ C52×C7×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3045

Polycyclic presentation:

2,3,5^2,7,29|c^a=c^4,d^a=d^4,f^a=f^28,c^b=cd,d^b=c^2d^3,e^b=e^2

Conjugacy classes & character table

892 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 67);