Finite Group Databasebeta

← Prev (#44478597) Next (#44478599) →

C2×C29×C7⋊(C52⋊C3) #44478598

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

Aliases

direct productC2×C29×C7⋊(C52⋊C3)
unambiguous semidirect product(C2×C7)⋊(C29×C52⋊C3)
unambiguous semidirect product(C2×C52)⋊(ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C2×C7×C29)⋊(C52⋊C3)
unambiguous semidirect product(C2×C52×C29)⋊ΓL(1,𝔽8)

Splittings

Fitting, socle, HallC2×C52×C7×C29 ⋊ C3
derived, HallC52×C7 ⋊ C2×C3×C29
HallC52×C7×C29 ⋊ C2×C3
HallC2×C52×C29 ⋊ ΓL(1,𝔽8)
HallC52×C29 ⋊ C2×ΓL(1,𝔽8)
HallC2×C7×C29 ⋊ C52⋊C3
HallC2×C52×C7 ⋊ C3×C29
HallC7×C29 ⋊ C2×C52⋊C3
HallC2×C52 ⋊ ΓL(1,𝔽8)×C29
SylowC52 ⋊ C2×ΓL(1,𝔽8)×C29
HallC2×C7 ⋊ C29×C52⋊C3
SylowC7 ⋊ C2×C29×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C29C7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7C2×C3×C29
FrattiniC1G
Fitting, socleC2×C52×C7×C29C3
LCSG ▷ C52×C7
UCSC1 ◁ C2×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6090

Conjugacy classes & character table

3538 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 82);