Finite Group Databasebeta

← Prev (#44541966) Next (#44541968) →

C4×C29×C11⋊C25 #44541967

order31900
automorphism?
homologyAbelianization (H1) = C4×C25×C29 · Schur multiplier (H2) = C1

Aliases

direct productC4×C29×C11⋊C25
unambiguous semidirect product(C4×C11)⋊(C25×C29)
unambiguous semidirect product(C4×C11×C29)⋊C25

Splittings

derived, SylowC11 ⋊ C4×C25×C29
HallC4×C11×C29 ⋊ C25
HallC11×C29 ⋊ C4×C25
HallC4×C11 ⋊ C25×C29

Subgroups

subgroupG/H
center, hypercenterC4×C5×C29C11⋊C5
commutator, hypocenterC11C4×C25×C29
FrattiniC2×C5C2×C29×C11⋊C5
FittingC4×C5×C11×C29C5
socle, prime radicalC2×C5×C11×C29C2×C5
cosocleC2×C5×C11C2×C5×C29
LCSG ▷ C11
UCSC1 ◁ C4×C5×C29

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31900

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, 2);