Finite Group Databasebeta

C2×#518×D67 #31762408

order17152
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#518×D67

Splittings

FittingC2×#518×C67 ⋊ C2
SylowC67 ⋊ C22×#518

Subgroups

subgroupG/H
centerC23C24×D67
commutatorC2×C67C25×C4
FrattiniC22C25×D67
FittingC2×#518×C67C2
socleC23×C67C25
prime radicalC23×D4×D67C2
cosocleC22×C67C26
hypercenterC2×#518D67
hypocenterC67C22×#518
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#518

14590 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1076145);