Finite Group Databasebeta

M16×#63247 #17964128

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

Aliases

direct productM16×#63247

Splittings

SylowC17 ⋊ M162

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×#595
commutator, socleC22×C17C22×C42
FittingC22×M16×C17C4
prime radicalC24×C17C42
cosocleC4×Dic17C24
hypercenterC22×M16#595
hypocenterC17M162
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×M16

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1099372);