Finite Group Databasebeta

C2×C4×#10587544 #17968489

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

Aliases

direct productC2×C4×#10587544

Splittings

SylowC17 ⋊ C2×C4×C4⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×#595
commutatorC2×C17C22×C4×C8
FrattiniC23C23×#595
FittingC22×C42×C17C4
socle, prime radicalC24×C17C22×C4
cosocleC22×Dic17C24
hypercenterC22×C42#595
hypocenterC17C2×C4×C4⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C22×C42

1550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

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, 1103733);