Finite Group Databasebeta

#1390×D67 #30770768

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct product#1390×D67

Splittings

FittingC67×#1390 ⋊ C2
SylowC67 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC22#99×D67
commutatorC23×C67C2×C42
FrattiniC22×D4C22×D67
FittingC67×#1390C2
socleC22×C67C2×#99
prime radicalC22×D4×D67C22
cosocleC22×D4×C67C23
hypercenter#1390D67
hypocenterC67C2×#1390
LCSG ▷ C23×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1390

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 84505);