Finite Group Databasebeta

C2×#21447540 #29832906

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447540

Splittings

SylowC61 ⋊ C2×#2141

Subgroups

subgroupG/H
centerC23C2×D488
commutatorC8×C61C23×C4
FrattiniC2×C8C23×D61
FittingC22×M32×C61C2
socleC23×C61C2×D8
prime radicalC24×C61D8
cosocleC2×C8×C61C24
hypercenterC22×M32D61
hypocenterC61C2×#2141
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 322461);