Finite Group Databasebeta

← Prev (#44542019) Next (#44542021) →

C4×C5×C29×C11⋊C5 #44542020

order31900
automorphism?
homologyAbelianization (H1) = C4×C52×C29 · Schur multiplier (H2) = C5

Aliases

direct productC4×C5×C29×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C52×C29)
unambiguous semidirect product(C4×C5×C11)⋊(C5×C29)
unambiguous semidirect product(C4×C11×C29)⋊C52
unambiguous semidirect product(C4×C5×C11×C29)⋊C5

Splittings

FittingC4×C5×C11×C29 ⋊ C5
derived, SylowC11 ⋊ C4×C52×C29
HallC4×C11×C29 ⋊ C52
HallC11×C29 ⋊ C4×C52
HallC4×C11 ⋊ C52×C29

Subgroups

subgroupG/H
center, hypercenterC4×C5×C29C11⋊C5
commutator, hypocenterC11C4×C52×C29
FrattiniC2C2×C5×C29×C11⋊C5
FittingC4×C5×C11×C29C5
socleC2×C5×C11×C29C2×C5
prime radicalC2×C5×C29×C11⋊C5C2
cosocleC2×C11C2×C52×C29
LCSG ▷ C11
UCSC1 ◁ C4×C5×C29

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6380

Conjugacy classes & character table

4060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31900, 55);