Finite Group Databasebeta

D61×#1271 #29567945

order15616
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productD61×#1271

Splittings

FittingC61×#1271 ⋊ C2
SylowC61 ⋊ C2×#1271

Subgroups

subgroupG/H
centerC23C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61C2×#1271
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 57500);