Finite Group Databasebeta

M16×#63223 #17000034

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productM16×#63223

Splittings

SylowC17 ⋊ M162

Subgroups

subgroupG/H
center, FrattiniC42C23×D17
commutator, socleC22×C17C22×C42
FittingC2×C4×M16×C17C2
prime radicalC24×C17C42
cosocleC42×C17C24
hypercenterC2×C4×M16D17
hypocenterC17M162
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C42 ◁ C2×C4×M16

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 135278);