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AGL(1,ℤ/16)×D67 #31009268

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,ℤ/16)×D67

Splittings

FittingC67×AGL(1,ℤ/16) ⋊ C2
SylowC67 ⋊ C2×AGL(1,ℤ/16)

Subgroups

subgroupG/H
centerC2#442×D67
commutatorC8×C67C23×C4
FrattiniC2×C8C23×D67
FittingC67×AGL(1,ℤ/16)C2
socleC2×C67C2×#442
prime radical#509×D67C2
cosocleC2×C8×C67C24
hypercenterAGL(1,ℤ/16)D67
hypocenterC67C2×AGL(1,ℤ/16)
LCSG ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ AGL(1,ℤ/16)

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1072

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323005);