Finite Group Databasebeta

C42×D4×D17 #17192512

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

Aliases

direct productC42×D4×D17

Splittings

FittingC42×D4×C17 ⋊ C2
SylowC17 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC42×D4×C17C2
socle, cosocleC23×C17C25
prime radicalC22×D4×D17C22
hypercenterC42×D4D17
hypocenterC17C2×C42×D4
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C42×D4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 327756);