Finite Group Databasebeta

#1664×D67 #30836997

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

Aliases

direct product#1664×D67

Splittings

FittingC67×#1664 ⋊ C2
SylowC67 ⋊ C2×#1664

Subgroups

subgroupG/H
centerC22#120×D67
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC67×#1664C2
socleC22×C67C2×#120
prime radicalC2×D4×D67D4
hypercenter#1664D67
hypocenterC67C2×#1664
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ #1664

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 150734);