Finite Group Databasebeta

#102×#3633 #17981617

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

Aliases

direct product#102×#3633

Splittings

FittingC17×#102 ⋊ C8
SylowC17 ⋊ C8×#102

Subgroups

subgroupG/H
centerC22D4×#3633
commutatorC4×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC17×#102C8
socleC22×C17C8×D4
prime radicalC2×D4×D17C2×C4
cosocleC2×C4×#595C23
hypercenter#102#3633
hypocenterC17C8×#102
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

606 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, 1116861);