Finite Group Databasebeta

#131×Dic34 #17898738

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#131×Dic34

Splittings

SylowC17 ⋊ Q8×#131

Subgroups

subgroupG/H
centerC2×C8C23×D17
commutator, socleC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC4×C17×#131C2
prime radicalC2×#41×C17C23
cosocleC2×C4×C17C25
hypercenterC4×#131D17
hypocenterC17Q8×#131
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C4×#131

1882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033982);