Finite Group Databasebeta

#1636×D67 #30831564

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#1636×D67

Splittings

FittingC67×#1636 ⋊ C2
SylowC67 ⋊ C2×#1636

Subgroups

subgroupG/H
centerC22#120×D67
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC67×#1636C2
socleC22×C67C2×#120
prime radicalC22×D67#120
hypercenter#1636D67
hypocenterC67C2×#1636
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ #1636

914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 145301);