Finite Group Databasebeta

C2×#21447990 #29834743

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

Aliases

direct productC2×#21447990

Splittings

SylowC61 ⋊ C2×#2230

Subgroups

subgroupG/H
centerC22#16840052
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#443C2
socleC22×C61#476
prime radicalC2×#135×C61C22
hypercenterC2×#443D61
hypocenterC61C2×#2230
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

1726 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 324298);