Finite Group Databasebeta

C2×#14531176 #17192605

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14531176

Splittings

FittingC2×C17×#376 ⋊ C2
SylowC17 ⋊ C2×#2283

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#376C2
socleC24×C17C24
prime radicalC24×D17C23
cosocleC23×C17C25
hypercenterC2×#376D17
hypocenterC17C2×#2283
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×#376

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327849);