Finite Group Databasebeta

← Prev (#13183343) Next (#13183345) →

C2×D5⋊(C11⋊C8) #13183344

order1760
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×D5⋊(C11⋊C8)
unambiguous semidirect productD5⋊(C2×C11⋊C8)

Splittings

derived, HallC5×C11 ⋊ C22×C8
SylowC11 ⋊ C2×D5⋊C8
SylowC5 ⋊ C22×C11⋊C8

Subgroups

subgroupG/H
center, hypercenterC2×C4C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C22×C8
FrattiniC2C22×C11⋊AGL(1,𝔽5)
FittingC2×C4×C5×C11C4
socleC22×C5×C11C2×C4
prime radicalC22×D5×C11C4
cosocleC11×Dic5C23
LCSG ▷ C5×C11
UCSC1 ◁ C2×C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 880

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1153);