Finite Group Databasebeta

C2×#22561373 #30883227

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22561373

Splittings

SylowC67 ⋊ C2×#2029

Subgroups

subgroupG/H
centerC23#14524011
commutator, cosocleC24×C67C24
FrattiniC24C23×D67
FittingC2×#379×C67C2
socleC23×C67#120
prime radicalC26×C67C22
hypercenterC2×#379D67
hypocenterC67C2×#2029
LCSG ▷ C24×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C25 ◁ C2×#379

2818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 196964);