Finite Group Databasebeta

#1604×D67 #30828000

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#1604×D67

Splittings

FittingC67×#1604 ⋊ C2
SylowC67 ⋊ C2×#1604

Subgroups

subgroupG/H
centerC22#120×D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC67×#1604C2
socleC22×C67C2×#120
prime radical#537×D67C2
hypercenter#1604D67
hypocenterC67C2×#1604
LCSG ▷ C22×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1604

1480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

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, 141737);