Finite Group Databasebeta

D61×#2884 #30543484

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productD61×#2884

Splittings

FittingC61×#2884 ⋊ C2
SylowC61 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC2C22×C22⋊C4×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC61×#2884C2
socleC2×C61C23×C22⋊C4
prime radicalC2×2−1+4×D61C2
cosocleC23×C61C25
hypercenter#2884D61
hypocenterC61C2×#2884
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×Q8 ◁ #2884

4818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033039);