Finite Group Databasebeta

#135×#3633 #17982862

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct product#135×#3633

Splittings

FittingC17×#135 ⋊ C8
SylowC17 ⋊ C8×#135

Subgroups

subgroupG/H
centerC4D4×#3633
commutatorC4×C17C23×C8
FrattiniC4C23×#3633
FittingC17×#135C8
socleC2×C17C2×C8×D4
prime radical#135×D17C4
cosocleC4×#595C24
hypercenter#135#3633
hypocenterC17C8×#135
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118106);