Finite Group Databasebeta

#2206×D67 #31010051

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#2206×D67

Splittings

FittingC67×#2206 ⋊ C2
SylowC67 ⋊ C2×#2206

Subgroups

subgroupG/H
centerC22C2×D8×D67
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC67×#2206C2
socleC22×C67C22×D8
hypercenter#2206D67
hypocenterC67C2×#2206
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323788);