Finite Group Databasebeta

C2×C4×#10587567 #17192513

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×#10587567

Splittings

FittingC2×C4×C22⋊C4×C17 ⋊ C2
SylowC17 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC23×C4C22×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC2×C4×C22⋊C4×C17C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
cosocleC23×C17C25
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C2×C42×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327757);