Finite Group Databasebeta

C2×#14528399 #17022015

order4352
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25×C8

Aliases

direct productC2×#14528399

Splittings

FittingC2×C82×C17 ⋊ C2
SylowC17 ⋊ C2×#1712

Subgroups

subgroupG/H
centerC23#10587560
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C82×C17C2
socleC23×C17#127
hypercenterC2×C82D17
hypocenterC17C2×#1712
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C82

1342 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 157259);