Finite Group Databasebeta

M16×Dic311 #34091645

order19904
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×Dic311

Splittings

SylowC311 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D311
commutatorC2×C311C2×C42
FittingC2×M16×C311C2
socleC22×C311C22×C4
prime radicalC23×C311C2×C4
cosocleC2×C4×C311C23
hypercenterC2×M16D311
hypocenterC311C4×M16
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C2×C4 ◁ C2×M16

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9952

Conjugacy classes & character table

3140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 500);