Finite Group Databasebeta

C2×#22570393 #31724062

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22570393

Splittings

FittingC2×#518×C67 ⋊ C2
SylowC67 ⋊ C2×#3118

Subgroups

subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#518×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863530C2
hypercenterC2×#518D67
hypocenterC67C2×#3118
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#518

2274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2308 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1037799);