Finite Group Databasebeta

#1659×D67 #30836948

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct product#1659×D67

Splittings

FittingC67×#1659 ⋊ C2
SylowC67 ⋊ C2×#1659

Subgroups

subgroupG/H
centerC22#120×D67
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC67×#1659C2
socleC22×C67C2×#120
prime radicalH(3,𝔽4)×D67C2
hypercenter#1659D67
hypocenterC67C2×#1659
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ #1659

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 150685);