Finite Group Databasebeta

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C2×#100×#1043 #72221356

order6400
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#100×#1043

Splittings

FittingC2×C52×#100 ⋊ C4
SylowC52 ⋊ C2×C4×#100

Subgroups

subgroupG/H
centerC22C22⋊C4×#1043
commutatorC22×C52C22×C42
FrattiniC2×C4C23×#1043
FittingC2×C52×#100C4
socleC22×C52C4×C22⋊C4
prime radicalC22×D4×C5⋊D5C22
cosocleC2×C4×C5⋊D5C24
hypercenterC2×#100#1043
hypocenterC52C2×C4×#100
LCSG ▷ C22×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

7880 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#453×#1043
maximal normal subgroup ofC2×#453×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.