Finite Group Databasebeta

← Prev (#44478591) Next (#44478593) →

C5×ΓL(1,𝔽8)×D145 #44478592

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D145
unambiguous semidirect productC5⋊(C5×ΓL(1,𝔽8)×D29)
unambiguous semidirect productC29⋊(C5×D5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D145)⋊(C3×C5)
unambiguous semidirect product(C5×C7×D145)⋊C3

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derivedC5×C7×C29 ⋊ C2×C3×C5
HallC52×ΓL(1,𝔽8)×C29 ⋊ C2
HallC5×C7×D145 ⋊ C3
HallC52×C29 ⋊ C2×ΓL(1,𝔽8)
HallΓL(1,𝔽8)×C29 ⋊ C5×D5
HallC52×ΓL(1,𝔽8) ⋊ D29
HallC7×C29 ⋊ C3×C5×D5
HallC52×C7 ⋊ C3×D29
SylowC29 ⋊ C5×D5×ΓL(1,𝔽8)
SylowC52 ⋊ ΓL(1,𝔽8)×D29
SylowC7 ⋊ C3×C5×D145

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D145
commutator, cosocle, hypocenterC5×C7×C29C2×C3×C5
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C5×C7×C29
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2030

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 76);