Finite Group Databasebeta

← Prev (#13043286) Next (#13043288) →

C2×D5⋊#356 #13043287

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊#356
unambiguous semidirect productD5⋊(C2×#356)

Splittings

SylowC5 ⋊ C22×#356

Subgroups

subgroupG/H
centerC22D5⋊#99
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC22×C5C2×#99
prime radicalC23×D5C22⋊C4
cosocleC2×Dic10C24
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5C22×#356
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×C4⋊Q8

1254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1113555);