Finite Group Databasebeta

← Prev (#72223488) Next (#72223490) →

C2×#13104049 #72223489

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#13104049

Splittings

FittingC22×C4×C52 ⋊ C2×C4
SylowC52 ⋊ C2×#386

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC22×C52C23×C4
FrattiniC22C22×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC22×#87877C2
cosocleC22×C5⋊D5C24
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C2×#386
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

3482 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal quotient of#72223490, #72223501, #72223547

GAP

Past the SmallGroups library coverage — no SmallGroups id.