Finite Group Databasebeta

C2×#22559506 #30836970

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22559506

Splittings

FittingC2×#490×C67 ⋊ C2
SylowC67 ⋊ C2×#1657

Subgroups

subgroupG/H
centerC23#14524011
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC2×#490×C67C2
socleC23×C67#120
prime radicalC2×#16863783C2
hypercenterC2×#490D67
hypocenterC67C2×#1657
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

1010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1096 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 150707);