Finite Group Databasebeta

M16×#63216 #17958035

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×#63216

Splittings

SylowC17 ⋊ C16×M16

Subgroups

subgroupG/H
center, FrattiniC42C22×#595
commutatorC2×C17C2×C4×C16
FittingC4×M16×C17C4
socleC22×C17C2×C4×C8
prime radicalC23×C17C4×C8
cosocleC4×#3622C23
hypercenterC4×M16#595
hypocenterC17C16×M16
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C42 ◁ C4×M16

306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1093279);