Finite Group Databasebeta

M16×Dic226 #28399527

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×Dic226

Splittings

SylowC113 ⋊ Q8×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D113
commutator, socleC22×C113C23×C4
FittingC4×M16×C113C2
prime radicalC23×C113C22×C4
cosocleC2×C4×C113C24
hypercenterC4×M16D113
hypocenterC113Q8×M16
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C4×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 13463);