Finite Group Databasebeta

M16×Dic61 #16839713

order3904
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×Dic61

Splittings

SylowC61 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D61
commutatorC2×C61C2×C42
FittingC2×M16×C61C2
socleC22×C61C22×C4
prime radicalC23×C61C2×C4
cosocleC2×C4×C61C23
hypercenterC2×M16D61
hypocenterC61C4×M16
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×M16

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 500);