Finite Group Databasebeta

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C22×#13104814 #72242687

order6400
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C5

Aliases

direct productC22×#13104814

Splittings

SylowC52 ⋊ C23×#97

Subgroups

subgroupG/H
centerC23×C4C2×#1044
commutatorC2×C52C23×C42
FrattiniC22C24×#1044
FittingC22×C42×C52C4
socleC24×C52C22×C4
prime radicalC24×C5⋊D5C2×C4
cosocleC2×#1039C25
hypercenterC22×C42#1044
hypocenterC52C23×#97
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23×C4 ◁ C22×C42

11252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

544 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×#72220669
maximal normal subgroup ofC22×#72220669

GAP

Past the SmallGroups library coverage — no SmallGroups id.