Finite Group Databasebeta

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C2×#72242228 #72253259

order6400
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#72242228

Splittings

SylowC52 ⋊ C2×#1383

Subgroups

subgroupG/H
centerC22#13100253
commutatorC52×C8C2×C42
FrattiniC2×C8C22×#1043
FittingC2×C52×#106C4
socleC22×C52#340
prime radicalC23×C5⋊D5SD16
cosocleC2×C8×C5⋊D5C23
hypercenterC2×#106#1043
hypocenterC52C2×#1383
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#106

2456 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×#365×#1043
maximal normal subgroup ofC2×#365×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.