Finite Group Databasebeta

C2×#22562189 #31009780

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

Aliases

direct productC2×#22562189

Splittings

FittingC2×#350×C67 ⋊ C2
SylowC67 ⋊ C2×#2195

Subgroups

subgroupG/H
centerC22#16863532
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC2×#350×C67C2
socleC22×C67#447
prime radicalC2×#16864213C2
hypercenterC2×#350D67
hypocenterC67C2×#2195
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131 ◁ C2×#350

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1894 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323517);