Finite Group Databasebeta

← Prev (#37564670) Next (#37564672) →

C11⋊C5×C49⋊C9 #37564671

order24255
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×C49⋊C9
unambiguous semidirect productC11⋊(C5×C49⋊C9)
unambiguous semidirect productC49⋊(C9×C11⋊C5)
unambiguous semidirect product(C49×C11⋊C5)⋊C9
unambiguous semidirect product(C11×C49⋊C9)⋊C5

Splittings

derived, HallC11×C49 ⋊ C5×C9
HallC11×C49⋊C9 ⋊ C5
HallC49×C11⋊C5 ⋊ C9
SylowC49 ⋊ C9×C11⋊C5
SylowC11 ⋊ C5×C49⋊C9

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×C49⋊C3
commutator, hypocenterC11×C49C5×C9
FrattiniC3×C7ΓL(1,𝔽8)×C11⋊C5
Fitting, cosocleC3×C11×C49C3×C5
socleC3×C7×C11C5×ΓL(1,𝔽8)
prime radicalC3×C7×C11⋊C5ΓL(1,𝔽8)
LCSG ▷ C11×C49
UCSC1 ◁ C3

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4851

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 2);