Finite Group Databasebeta

C2×#11717196 #13107006

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

Aliases

direct productC2×#11717196

Splittings

FittingC2×C42×C52 ⋊ C2
SylowC52 ⋊ C2×#126

Subgroups

subgroupG/H
centerC23C22×C5⋊D5
commutator, cosocleC22×C52C24
FrattiniC22C23×C5⋊D5
FittingC2×C42×C52C2
socleC23×C52C23
prime radicalC23×C5⋊D5C22
hypercenterC2×C42C5⋊D5
hypocenterC52C2×#126
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C42

984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9358);