Finite Group Databasebeta

#99×#3624 #17951802

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#99×#3624

Splittings

SylowC17 ⋊ C8×#99

Subgroups

subgroupG/H
centerC22C22⋊C4×#595
commutatorC22×C17C2×C4×C8
FrattiniC24C22×#595
FittingC2×C17×#99C4
socleC22×C17C4×C22⋊C4
prime radicalC22×D4×C17C2×C4
cosocleC23×Dic17C23
hypercenterC2×#99#595
hypocenterC17C8×#99
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1087046);