Finite Group Databasebeta

C22×#16863657 #31723202

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#16863657

Splittings

SylowC67 ⋊ C22×#471

Subgroups

subgroupG/H
centerC23#14524015
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC22×AGL(1,ℤ/8)×C67C2
socleC23×C67#121
hypercenterC22×AGL(1,ℤ/8)D67
hypocenterC67C22×#471
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

2758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1036939);