Finite Group Databasebeta

C2×#22559159 #30827899

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22559159

Splittings

FittingC2×#448×C67 ⋊ C2
SylowC67 ⋊ C2×#1601

Subgroups

subgroupG/H
centerC23#14524011
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#448×C67C2
socleC23×C67#120
prime radicalC2×#16863954C2
hypercenterC2×#448D67
hypocenterC67C2×#1601
LCSG ▷ C22×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

1652 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 141636);