Finite Group Databasebeta

C2×#22574699 #31763543

order17152
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#22574699

Splittings

SylowC67 ⋊ C2×#3555

Subgroups

subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#529×C67C2
socleC23×C67C25
prime radicalC2×#121×C67C22
hypercenterC2×#529D67
hypocenterC67C2×#3555
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#529

6446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1077280);