Finite Group Databasebeta

C2×C5×#4092 #13106967

order1600
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#4092

Splittings

FittingC22×C52×Q8 ⋊ C2
SylowC52 ⋊ C2×C22⋊Q8

Subgroups

subgroupG/H
centerC23×C5C22×D5
commutator, cosocleC22×C5C24×C5
FrattiniC22C23×C5×D5
FittingC22×C52×Q8C2
socleC23×C52C23
prime radicalC23×C5×D5C22
hypercenterC22×C5×Q8D5
hypocenterC5C2×C5×C22⋊Q8
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C5 ◁ C22×C5×Q8

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9319);