Finite Group Databasebeta

M16×#6122 #16792723

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productM16×#6122

Splittings

SylowC13 ⋊ M162

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C22×C42
FittingC22×C13×M16C4
prime radicalC24×C13C42
cosocleC4×Dic13C24
hypercenterC22×M16#261
hypocenterC13M162
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1099372);