Finite Group Databasebeta

D61×#1305 #29570341

order15616
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productD61×#1305

Splittings

FittingC61×#1305 ⋊ C2
SylowC61 ⋊ C2×#1305

Subgroups

subgroupG/H
centerC22#95×D61
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1305C2
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1305D61
hypocenterC61C2×#1305
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

986 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 59896);