Finite Group Databasebeta

C2×C4×#10587558 #17192510

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×C4×#10587558

Splittings

FittingC2×C43×C17 ⋊ C2
SylowC17 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC22×C42C2×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC2×C43×C17C2
socleC24×C17C24
prime radicalC24×D17C23
cosocleC23×C17C25
hypercenterC2×C43D17
hypocenterC17C2×C4×#117
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C42 ◁ C2×C43

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327754);