Finite Group Databasebeta

#394×Dic17 #16956121

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct product#394×Dic17

Splittings

SylowC17 ⋊ C4×#394

Subgroups

subgroupG/H
center, FrattiniC24C23×D17
commutatorC23×C17C23×C4
FittingC2×C17×#394C2
socle, cosocleC24×C17C24
prime radicalC23×D4×C17C22
hypercenterC2×#394D17
hypocenterC17C4×#394
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#394

2550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 91365);