Finite Group Databasebeta

D61×#1377 #29594870

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productD61×#1377

Splittings

FittingC61×#1377 ⋊ C2
SylowC61 ⋊ C2×#1377

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC22×C61C2×C4×C8
FrattiniC22×C8C22×D61
FittingC61×#1377C2
socleC22×C61C2×C22⋊C8
prime radicalC23×D61C2×C8
cosocleC22×C8×C61C23
hypercenter#1377D61
hypocenterC61C2×#1377
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1377

630 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, 84425);