Finite Group Databasebeta

C2×#14527025 #16955982

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14527025

Splittings

SylowC17 ⋊ C2×#1438

Subgroups

subgroupG/H
centerC25C22×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
Fitting, prime radicalC24×D4×C17C2
socleC25×C17C23
cosocleC24×C17C24
hypercenterC24×D4D17
hypocenterC17C2×#1438
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C25 ◁ C24×D4

8190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 91226);