Finite Group Databasebeta

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C2×#72253151 #72269241

order6400
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#72253151

Splittings

FittingC2×C52×#135 ⋊ C4
SylowC52 ⋊ C22×#360

Subgroups

subgroupG/H
centerC22C2×#11716875
commutatorC52×C8C23×C4
FrattiniC8C23×#1043
FittingC2×C52×#135C4
socleC22×C52C2×#102
prime radicalC2×#135×C5⋊D5C2
cosocleC8×C5⋊D5C24
hypercenterC2×#135#1043
hypocenterC52C22×#360
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

4856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 800

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#360×#1043
maximal normal subgroup ofC2×#360×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.