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C2×D4×AGL(1,ℤ/16) #72285697

order2048
nilpotency class4
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×D4×AGL(1,ℤ/16)

Subgroups

subgroupG/H
center, socleC23C22×#442
commutatorC2×C8C25×C4
Frattini, cosocleC22×C8C26
prime radicalC2×D4×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×D4 ◁ C2×D4×#97 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

33172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 128

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD4×#495725, C22×D4×AGL(1,ℤ/16), C2×#72265256, …
maximal normal subgroup ofD4×#495725, C22×D4×AGL(1,ℤ/16), C2×#72265256, …
maximal quotient ofC2×D4×#12067, C2×#72257081, D4×#495725, …
automorphism group of#33859

GAP

Past the SmallGroups library coverage — no SmallGroups id.