Finite Group Databasebeta

C2×#22558075 #30745672

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22558075

Splittings

SylowC67 ⋊ C2×#1288

Subgroups

subgroupG/H
centerC23C67⋊#95
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC2×#432×C67C2
socleC23×C67#95
prime radicalC24×C67C22⋊C4
cosocleC2×C42×C67C23
hypercenterC2×#432D67
hypocenterC67C2×#1288
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#432

678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59409);