Finite Group Databasebeta

#1698×D67 #30838475

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

Aliases

direct product#1698×D67

Splittings

FittingC67×#1698 ⋊ C2
SylowC67 ⋊ C2×#1698

Subgroups

subgroupG/H
centerC22#121×D67
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC67×#1698C2
socleC22×C67C2×#121
prime radical#127×D67C22
hypercenter#1698D67
hypocenterC67C2×#1698
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ #1698

702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 152212);