Finite Group Databasebeta

← Prev (#72242684) Next (#72242686) →

C22×#11717448 #72242685

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C5

Aliases

direct productC22×#11717448

Splittings

SylowC52 ⋊ C23×M16

Subgroups

subgroupG/H
centerC22×C4C2×#1044
commutatorC2×C52C24×C4
FrattiniC2C24×#1044
FittingC23×C4×C52C4
socleC23×C52C22×C4
prime radicalC24×C5⋊D5C4
cosocle#1039C25
hypercenterC23×C4#1044
hypocenterC52C23×M16
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C4 ◁ C23×C4

4802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×#13103905
maximal normal subgroup ofC22×#13103905
maximal quotient ofC22×#13104814

GAP

Past the SmallGroups library coverage — no SmallGroups id.