Finite Group Databasebeta

← Prev (#34035164) Next (#34035166) →

C5×C11⋊C5×Dic17 #34035165

order18700
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C11⋊C5×Dic17
unambiguous semidirect product(C11×Dic17)⋊C52
unambiguous semidirect product(C5×C11×Dic17)⋊C5

Splittings

derived, HallC11×C17 ⋊ C4×C52
HallC5×C17×C11⋊C5 ⋊ C4
HallC11×Dic17 ⋊ C52
SylowC17 ⋊ C4×C5×C11⋊C5
SylowC11 ⋊ C52×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C5D17×C11⋊C5
commutator, hypocenterC11×C17C4×C52
FrattiniC2C5×D17×C11⋊C5
Fitting, socleC2×C5×C11×C17C2×C5
prime radicalC2×C5×C17×C11⋊C5C2
cosocleC2×C11×C17C2×C52
LCSG ▷ C11×C17
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3740

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 50);