Finite Group Databasebeta

C4×#11763810 #17968488

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11763810

Splittings

SylowC17 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC2×C42C2×#595
commutatorC2×C17C22×C4×C8
FrattiniC23C23×#595
FittingC43×C17C4
socleC23×C17C23×C4
prime radicalC23×D17C22×C4
cosocleC22×Dic17C24
hypercenterC43#595
hypocenterC17C2×C4×C4⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C43

1550 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, 1103732);