Finite Group Databasebeta

C2×#21448309 #29838403

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

Aliases

direct productC2×#21448309

Splittings

FittingC23×C42×C61 ⋊ C2
SylowC61 ⋊ C2×#2297

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC23×C42×C61C2
socleC24×C61C24
prime radicalC23×#11758222C2
cosocleC23×C61C25
hypercenterC23×C42D61
hypocenterC61C2×#2297
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C23×C42

6174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

3952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 327958);