Finite Group Databasebeta

C4×#11763895 #17981602

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#11763895

Splittings

FittingC2×C42×C17 ⋊ C8
SylowC17 ⋊ C4×#324

Subgroups

subgroupG/H
centerC2×C4C22⋊#3633
commutatorC22×C17C2×C4×C8
FrattiniC23C22×#3633
FittingC2×C42×C17C8
socleC22×C17C2×C22⋊C8
prime radicalC23×D17C22×C4
cosocleC23×#595C23
hypercenterC2×C42#3633
hypocenterC17C4×#324
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116846);