Finite Group Databasebeta

#1693×D67 #30838356

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C23×C4

Aliases

direct product#1693×D67

Splittings

FittingC67×#1693 ⋊ C2
SylowC67 ⋊ C2×#1693

Subgroups

subgroupG/H
centerC22#121×D67
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC67×#1693C2
socleC22×C67C2×#121
prime radicalC2×D4×D67D4
hypercenter#1693D67
hypocenterC67C2×#1693
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ #1693

758 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, 152093);