Finite Group Databasebeta

C2×#13105101 #72269229

order3200
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#13105101

Splittings

FittingC2×C42×C52 ⋊ C22
SylowC52 ⋊ C22×#124

Subgroups

subgroupG/H
centerC23C22×D52
commutator, cosocleC22×C52C25
FrattiniC22C23×D52
FittingC2×C42×C52C22
socleC23×C52C24
prime radicalC22×#87877C2
hypercenterC2×C42D52
hypocenterC52C22×#124
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C42

4258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.