Finite Group Databasebeta

C2×#14526769 #16944465

order4352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#14526769

Splittings

SylowC17 ⋊ C2×#1339

Subgroups

subgroupG/H
centerC22#11762543
commutatorC2×C8×C17C22×C4
FrattiniC2×M16C22×D17
Fitting, prime radicalC2×C17×#469C2
socleC22×C17#327
cosocleC2×M16×C17C23
hypercenterC2×#469D17
hypocenterC17C2×#1339
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#469

496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 79709);