Finite Group Databasebeta

C2×#22572690 #31734406

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

Aliases

direct productC2×#22572690

Splittings

FittingC22×#107×C67 ⋊ C2
SylowC67 ⋊ C2×#3346

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC22×#107×C67C2
socleC23×C67C22×D4
prime radicalC2×#16864094C2
hypercenterC22×#107D67
hypocenterC67C2×#3346
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

1942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1906 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1048143);