Finite Group Databasebeta

D61×#1280 #29569599

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productD61×#1280

Splittings

FittingC61×#1280 ⋊ C2
SylowC61 ⋊ C2×#1280

Subgroups

subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C61C2×C4×C8
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61C2×#1280
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59154);