Finite Group Databasebeta

C2×#22561364 #30883190

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

Aliases

direct productC2×#22561364

Splittings

FittingC2×#339×C67 ⋊ C2
SylowC67 ⋊ C2×#2027

Subgroups

subgroupG/H
centerC23#14524013
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#339×C67C2
socleC23×C67#120
prime radicalC23×D268C22
hypercenterC2×#339D67
hypocenterC67C2×#2027
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 196927);