Finite Group Databasebeta

#417×Dic17 #17032118

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct product#417×Dic17

Splittings

SylowC17 ⋊ C4×#417

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutatorC4×C17C22×C42
FrattiniC22×C4C23×D17
FittingC2×C17×#417C2
socleC23×C17C22×D4
prime radicalC22×#41×C17C22
cosocleC22×C4×C17C24
hypercenterC2×#417D17
hypocenterC17C4×#417
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

1706 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, 167362);