Finite Group Databasebeta

← Prev (#72253239) Next (#72253241) →

C2×#13104749 #72253240

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13104749

Splittings

FittingC2×C52×SD16 ⋊ C4
SylowC52 ⋊ C2×#444

Subgroups

subgroupG/H
centerC22D4×#1043
commutatorC4×C52C23×C4
FrattiniC4C23×#1043
FittingC2×C52×SD16C4
socleC22×C52C4×D4
prime radicalC2×#11717236C2
cosocleC4×C5⋊D5C24
hypercenterC2×SD16#1043
hypocenterC52C2×#444
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

1856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72253147
maximal normal subgroup ofC2×#72253147

GAP

Past the SmallGroups library coverage — no SmallGroups id.