Finite Group Databasebeta

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C22×#11717353 #72242652

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11717353

Splittings

SylowC52 ⋊ C22×C4×Q8

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C24×C4
FrattiniC2C23×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC23×C5⋊D5C23
cosocleC2×C5⋊D5C25
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C22×C4×Q8
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

3826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×#13107568
maximal normal subgroup ofC22×#13107568

GAP

Past the SmallGroups library coverage — no SmallGroups id.