Finite Group Databasebeta

C2×#14531510 #17193128

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#14531510

Splittings

SylowC17 ⋊ C2×#2328

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
Fitting, prime radicalC22×C17×#127C2
socleC24×C17C24
cosocleC23×C17C25
hypercenterC22×#127D17
hypocenterC17C2×#2328
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#127

4430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328372);