Finite Group Databasebeta

#97×#3633 #17981559

order4352
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct product#97×#3633

Splittings

FittingC17×#97 ⋊ C8
SylowC17 ⋊ C8×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×#3633
commutatorC2×C17C42×C8
FittingC17×#97C8
socleC22×C17C2×C4×C8
prime radicalC22×D17C2×C42
cosocleC2×C4×#595C23
hypercenter#97#3633
hypocenterC17C8×#97
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #97

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1116803);