Finite Group Databasebeta

M16×Dic47 #15689074

order3008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×Dic47

Splittings

SylowC47 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D47
commutatorC2×C47C2×C42
FittingC2×M16×C47C2
socleC22×C47C22×C4
prime radicalC23×C47C2×C4
cosocleC2×C4×C47C23
hypercenterC2×M16D47
hypocenterC47C4×M16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×M16

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 500);