Finite Group Databasebeta

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C22×C5×#3935 #72242657

order3200
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C26

Aliases

direct productC22×C5×#3935

Splittings

SylowC52 ⋊ C22×#97

Subgroups

subgroupG/H
centerC23×C4×C5C2×D5
commutatorC2×C5C22×C42×C5
FrattiniC2×C4C23×C5×D5
FittingC22×C42×C52C2
socle, prime radicalC24×C52C2×C4
cosocleC2×C4×C5C24×C5
hypercenterC22×C42×C5D5
hypocenterC5C22×C5×#97
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4×C5 ◁ C22×C42×C5

1858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×#13100501
maximal normal subgroup ofC22×#13100501

GAP

Past the SmallGroups library coverage — no SmallGroups id.