Finite Group Databasebeta

← Prev (#44542039) Next (#44542041) →

AGL(1,𝔽5)×C29×C11⋊C5 #44542040

order31900
automorphism?
homologyAbelianization (H1) = C4×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C29×C11⋊C5
unambiguous semidirect product(C11×AGL(1,𝔽5))⋊(C5×C29)
unambiguous semidirect product(C11×AGL(1,𝔽5)×C29)⋊C5

Splittings

Fitting, socleC5×C11×C29 ⋊ C4×C5
derivedC5×C11 ⋊ C4×C5×C29
HallC5×C29×C11⋊C5 ⋊ C4
HallC11×C29 ⋊ C5×AGL(1,𝔽5)
HallC5×C11⋊C5 ⋊ C4×C29
SylowC11 ⋊ C5×AGL(1,𝔽5)×C29

Subgroups

subgroupG/H
center, hypercenterC29AGL(1,𝔽5)×C11⋊C5
commutator, hypocenterC5×C11C4×C5×C29
FrattiniC1G
Fitting, socleC5×C11×C29C4×C5
prime radicalD5×C29×C11⋊C5C2
cosocleD5×C11C2×C5×C29
LCSG ▷ C5×C11
UCSC1 ◁ C29

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1595

Conjugacy classes & character table

1015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 75);