Finite Group Databasebeta

C2×#21462255 #30624546

order15616
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#21462255
unambiguous semidirect productD61⋊#2273

Splittings

FittingC22×C22⋊C4×C61 ⋊ C4
SylowC61 ⋊ C2×#2273

Subgroups

subgroupG/H
centerC23C23×#6923
commutatorC2×C61C23×C42
FrattiniC22C24×#6923
FittingC22×C22⋊C4×C61C4
socleC23×C61C23×C4
prime radicalC25×D61C22
cosocleC22×D61C25
hypercenterC22×C22⋊C4#6923
hypocenterC61C2×#2273
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C22⋊C4

5790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114101);