Finite Group Databasebeta

D61×#1556 #29648529

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productD61×#1556

Splittings

FittingC61×#1556 ⋊ C2
SylowC61 ⋊ C2×#1556

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1556C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1556D61
hypocenterC61C2×#1556
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

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, 138084);