Finite Group Databasebeta

C4×#16839543 #29595054

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16839543

Splittings

FittingC4×M32×C61 ⋊ C2
SylowC61 ⋊ C4×#349

Subgroups

subgroupG/H
centerC42#11758198
commutatorC22×C61C2×C4×C8
FrattiniC22×C8C22×D61
FittingC4×M32×C61C2
socleC22×C61C2×C22⋊C8
prime radicalC23×D61C2×C8
cosocleC22×C8×C61C23
hypercenterC4×M32D61
hypocenterC61C4×#349
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C4×M32

522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 84609);