Finite Group Databasebeta

C2×C4×M16×D61 #30543397

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×M16×D61

Splittings

FittingC2×C4×M16×C61 ⋊ C2
SylowC61 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC2×C42C22×D61
commutatorC2×C61C23×C42
FrattiniC2×C4C24×D61
FittingC2×C4×M16×C61C2
socleC23×C61C23×C4
prime radicalC24×D61C2×C4
cosocleC2×C4×C61C25
hypercenterC2×C4×M16D61
hypocenterC61C22×C4×M16
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1032952);