Finite Group Databasebeta

← Prev (#72253169) Next (#72253171) →

C2×#442×#1043 #72253170

order12800
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#442×#1043

Splittings

FittingC2×C52×#442 ⋊ C4
SylowC52 ⋊ C2×C4×#442

Subgroups

subgroupG/H
centerC23C2×D4×#1043
commutatorC4×C52C23×C42
FrattiniC2×C4C24×#1043
FittingC2×C52×#442C4
socleC23×C52C2×C4×D4
prime radicalC22×D8×C5⋊D5C22
cosocleC2×C4×C5⋊D5C25
hypercenterC2×#442#1043
hypocenterC52C2×C4×#442
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

33040 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.

GAP

Past the SmallGroups library coverage — no SmallGroups id.