Finite Group Databasebeta

C4×#11763858 #17968854

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11763858

Splittings

SylowC17 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC23C23×#595
FittingC4×C4⋊C4×C17C4
socle, prime radicalC23×C17C23×C4
cosocleC22×Dic17C24
hypercenterC4×C4⋊C4#595
hypocenterC17C4×C8×Q8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1104098);