Finite Group Databasebeta

C2×#14527869 #17010208

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14527869

Splittings

FittingC2×C17×D4⋊C8 ⋊ C2
SylowC17 ⋊ C2×#1624

Subgroups

subgroupG/H
centerC23#10587568
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C17×D4⋊C8C2
socleC23×C17#120
hypercenterC2×D4⋊C8D17
hypocenterC17C2×#1624
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 145452);