Finite Group Databasebeta

← Prev (#72253248) Next (#72253250) →

C2×#444×#1043 #72253249

order12800
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#444×#1043

Splittings

FittingC2×C52×#444 ⋊ C4
SylowC52 ⋊ C2×C4×#444

Subgroups

subgroupG/H
centerC2×C4C2×D4×#1043
commutatorC4×C52C23×C42
FrattiniC2×C4C24×#1043
FittingC2×C52×#444C4
socleC22×C52C42×D4
prime radicalC2×#135×C5⋊D5C22
cosocleC2×C4×C5⋊D5C25
hypercenterC2×#444#1043
hypocenterC52C2×C4×#444
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#444

24752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.