Finite Group Databasebeta

M16×Dic461 #44442027

order29504
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×Dic461

Splittings

SylowC461 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D461
commutatorC2×C461C2×C42
FittingC2×M16×C461C2
socleC22×C461C22×C4
prime radicalC23×C461C2×C4
cosocleC2×C4×C461C23
hypercenterC2×M16D461
hypocenterC461C4×M16
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C2×C4 ◁ C2×M16

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

4640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 500);