Finite Group Databasebeta

#1779×D67 #30854933

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C29

Aliases

direct product#1779×D67

Splittings

FittingC67×#1779 ⋊ C2
SylowC67 ⋊ C2×#1779

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D67
commutatorC22×C67C23×C8
FittingC67×#1779C2
socleC23×C67C23×C4
prime radicalC25×D67C4
cosocleC22×C4×C67C24
hypercenter#1779D67
hypocenterC67C2×#1779
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ #1779

6110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 168670);