Finite Group Databasebeta

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C2×#13104740 #72220829

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

Aliases

direct productC2×#13104740

Splittings

FittingC2×C52×M16 ⋊ C4
SylowC52 ⋊ C2×#428

Subgroups

subgroupG/H
centerC22C2×C4⋊#1043
commutatorC4×C52C23×C4
FrattiniC4C23×#1043
FittingC2×C52×M16C4
socleC22×C52C2×C4⋊C4
prime radicalC23×C5⋊D5D4
cosocleC4×C5⋊D5C24
hypercenterC2×M16#1043
hypocenterC52C2×#428
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

2144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221002, C2×AGL(1,ℤ/8)×#1043, #72221132, …
maximal normal subgroup of#72221002, C2×AGL(1,ℤ/8)×#1043, #72221132, …
maximal quotient of#72221002, #72223096, C2×#72220671

GAP

Past the SmallGroups library coverage — no SmallGroups id.