Finite Group Databasebeta

#104×Dic34 #17051021

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#104×Dic34

Splittings

SylowC17 ⋊ Q8×#104

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC4×C17×#104C2
socleC22×C17C22×C22⋊C4
prime radicalC2×#41×C17C23
cosocleC22×C4×C17C24
hypercenterC4×#104D17
hypocenterC17Q8×#104
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#104

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 186265);