Finite Group Databasebeta

C2×#21445728 #29679116

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#21445728

Splittings

FittingC22×C22⋊C8×C61 ⋊ C2
SylowC61 ⋊ C2×#1779

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C23×C8
FrattiniC22×C4C23×D61
FittingC22×C22⋊C8×C61C2
socleC24×C61C22×C4
prime radicalC25×D61C4
cosocleC22×C4×C61C24
hypercenterC22×C22⋊C8D61
hypocenterC61C2×#1779
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

6110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 168671);