Finite Group Databasebeta

C2×#22574027 #31764162

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

Aliases

direct productC2×#22574027

Splittings

FittingC2×Q82×C67 ⋊ C2
SylowC67 ⋊ C2×#3503

Subgroups

subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×Q82×C67C2
socleC23×C67C25
prime radicalC22×#11761629C22
hypercenterC2×Q82D67
hypocenterC67C2×#3503
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×Q82

7478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1738 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1077899);