Finite Group Databasebeta

C2×#21462311 #30624625

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×#21462311
unambiguous semidirect productD61⋊#2328

Splittings

FittingC2×#127×C61 ⋊ C4
SylowC61 ⋊ C2×#2328

Subgroups

subgroupG/H
centerC23C23×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC2×#127×C61C4
socleC23×C61C23×C4
prime radicalC2×#127×D61C2
cosocleC22×D61C25
hypercenterC2×#127#6923
hypocenterC61C2×#2328
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#127

4430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114180);