Finite Group Databasebeta

← Prev (#13183223) Next (#13183225) →

C2×C4⋊Dic55 #13183224

order1760
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊Dic55

Splittings

HallC5×C11 ⋊ C2×C4⋊C4
SylowC11 ⋊ C2×C4⋊Dic5
SylowC5 ⋊ C2×C4⋊Dic11

Subgroups

subgroupG/H
centerC23C2×D55
commutatorC2×C5×C11C22×C4
FrattiniC22C22×D55
FittingC22×C4×C5×C11C2
socle, prime radicalC23×C5×C11C22
cosocleC22×C5×C11C23
hypercenterC22×C4D55
hypocenterC5×C11C2×C4⋊C4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C23 ◁ C22×C4

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1760

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1033);