Finite Group Databasebeta

C4×#41×Dic17 #17192526

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#41×Dic17

Splittings

SylowC17 ⋊ C42×#41

Subgroups

subgroupG/H
centerC2×C42C22×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC2×C4×#41×C17C2
socle, cosocleC23×C17C25
prime radicalC22×#41×C17C22
hypercenterC2×C4×#41D17
hypocenterC17C42×#41
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C2×C4×#41

4086 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, 327770);