Finite Group Databasebeta

← Prev (#34035117) Next (#34035119) →

C17×Dic11⋊C25 #34035118

order18700
automorphism?
homologyAbelianization (H1) = C4×C17×C25 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic11⋊C25
unambiguous semidirect productDic11⋊(C17×C25)
unambiguous semidirect product(C11⋊C25)⋊(C4×C17)
unambiguous semidirect product(C17×Dic11)⋊C25

Splittings

derived, SylowC11 ⋊ C4×C17×C25
HallC17×C11⋊C25 ⋊ C4
HallC17×Dic11 ⋊ C25
HallC11⋊C25 ⋊ C4×C17
HallC11×C17 ⋊ C4×C25
HallDic11 ⋊ C17×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17AGL(1,𝔽11)
commutator, hypocenterC11C4×C17×C25
FrattiniC2×C5C17×AGL(1,𝔽11)
Fitting, socle, prime radicalC2×C5×C11×C17C2×C5
cosocleC2×C5×C11C2×C5×C17
LCSG ▷ C11
UCSC1 ◁ C2×C5×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18700

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 3);