Finite Group Databasebeta

C2×Q82×D67 #31762896

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

Aliases

direct productC2×Q82×D67

Splittings

FittingC2×Q82×C67 ⋊ C2
SylowC67 ⋊ C22×Q82

Subgroups

subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×Q82×C67C2
socleC23×C67C25
prime radicalC23×D67C24
hypercenterC2×Q82D67
hypocenterC67C22×Q82
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×Q82

7846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1076633);