Finite Group Databasebeta

#3175×D67 #31725645

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#3175×D67

Splittings

FittingC67×#3175 ⋊ C2
SylowC67 ⋊ C2×#3175

Subgroups

subgroupG/H
centerC22C22×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC67×#3175C2
socleC22×C67C23×D4
prime radical#466×D67C2
hypercenter#3175D67
hypocenterC67C2×#3175
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ #117 ◁ #3175

1970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1039382);