Finite Group Databasebeta

← Prev (#13183111) Next (#13183113) →

C2×C8×D5×C11 #13183112

order1760
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23

Aliases

direct productC2×C8×D5×C11

Splittings

FittingC2×C5×C8×C11 ⋊ C2
derived, SylowC5 ⋊ C22×C8×C11
HallC5×C11 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8×C11D5
commutator, hypocenterC5C22×C8×C11
FrattiniC4C22×D5×C11
FittingC2×C5×C8×C11C2
socleC22×C5×C11C2×C4
prime radicalC22×D5×C11C4
cosocleC4×C5C23×C11
LCSG ▷ C5
UCSC1 ◁ C2×C8×C11

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 880

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 921);