Finite Group Databasebeta

C2×#22569819 #31722967

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22569819

Splittings

FittingC2×#427×C67 ⋊ C2
SylowC67 ⋊ C2×#3054

Subgroups

subgroupG/H
centerC22×C4D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#427×C67C2
socleC23×C67C22×D4
hypercenterC2×#427D67
hypocenterC67C2×#3054
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#427

2918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1036704);