Finite Group Databasebeta

C4×#11763741 #17962546

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#11763741

Splittings

SylowC17 ⋊ C4×M64

Subgroups

subgroupG/H
centerC4×C8C2×#595
commutatorC2×C17C2×C4×C16
FrattiniC2×C8C22×#595
FittingC2×C4×C8×C17C4
socleC22×C17C22×C16
prime radicalC23×C17C2×C16
cosocleC2×#63214C23
hypercenterC2×C4×C8#595
hypocenterC17C4×M64
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1097790);