Finite Group Databasebeta

C2×C4×#10587549 #17968437

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#10587549

Splittings

FittingC2×C4×Q8×C17 ⋊ C4
SylowC17 ⋊ C2×C4×#103

Subgroups

subgroupG/H
centerC22×C4C22⋊#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C4×Q8×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C2×D4
cosocleC2×C4×D17C24
hypercenterC2×C4×Q8#595
hypocenterC17C2×C4×#103
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

1726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1103681);