Finite Group Databasebeta

C2×#21447749 #29833756

order15616
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21447749

Splittings

FittingC2×C61×#357 ⋊ C2
SylowC61 ⋊ C2×#2187

Subgroups

subgroupG/H
centerC23D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#357C2
socleC23×C61C2×D8
prime radicalC22×D8×D61C2
hypercenterC2×#357D61
hypocenterC61C2×#2187
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

1382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1378 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 323311);