Finite Group Databasebeta

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C2×M16×#1043 #72220825

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×#1043

Splittings

FittingC2×C52×M16 ⋊ C4
SylowC52 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C4C22×#1043
commutatorC2×C52C22×C42
FrattiniC4C23×#1043
FittingC2×C52×M16C4
socleC22×C52C2×C42
prime radicalC23×C5⋊D5C2×C4
cosocleC4×C5⋊D5C24
hypercenterC2×M16#1043
hypocenterC52C2×C4×M16
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C2×M16

2624 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×M16×#1043, C2×AGL(1,ℤ/8)×#1043, #72221132, …
maximal normal subgroup ofC4×M16×#1043, C2×AGL(1,ℤ/8)×#1043, #72221132, …
maximal quotient ofC4×M16×#1043, #72221173, C2×#97×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.