Finite Group Databasebeta

← Prev (#72253178) Next (#72253180) →

#1043×#1580 #72253179

order12800
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct product#1043×#1580

Splittings

FittingC52×#1580 ⋊ C4
SylowC52 ⋊ C4×#1580

Subgroups

subgroupG/H
centerC2×C4C2×D4×#1043
commutatorC4×C52C22×C4×C8
FrattiniC42C23×#1043
FittingC52×#1580C4
socleC22×C52C42×D4
prime radicalC2×D8×C5⋊D5C2×C4
cosocleC42×C5⋊D5C24
hypercenter#1580#1043
hypocenterC52C4×#1580
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

8336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1600

Conjugacy classes & character table

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

Relationships

maximal subgroup of#1043×#12067
maximal normal subgroup of#1043×#12067
maximal quotient of#1043×#12067

GAP

Past the SmallGroups library coverage — no SmallGroups id.