Finite Group Databasebeta

M16×#6094 #15828627

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

Aliases

direct productM16×#6094

Splittings

FittingC8×C13×M16 ⋊ C2
SylowC13 ⋊ M162

Subgroups

subgroupG/H
center, FrattiniC42C23×D13
commutator, socleC22×C13C22×C42
FittingC8×C13×M16C2
prime radicalC23×D13C42
cosocleC42×C13C24
hypercenterC8×M16D13
hypocenterC13M162
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C42 ◁ C8×M16

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135276);