Finite Group Databasebeta

#137×#3622 #17003751

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

Aliases

direct product#137×#3622

Splittings

SylowC17 ⋊ C8×#137

Subgroups

subgroupG/H
centerC2×C4C2×D4×D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC4×C17×#137C2
socleC22×C17C2×C4×D4
prime radicalC2×#41×C17C2×C4
cosocleC42×C17C24
hypercenterC4×#137D17
hypocenterC17C8×#137
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#137

714 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, 138995);