Finite Group Databasebeta

C2×#21461484 #30613843

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC2×#21461484

Splittings

FittingC23×C8×C61 ⋊ C4
SylowC61 ⋊ C2×#1729

Subgroups

subgroupG/H
centerC22×C4C22×#6923
commutatorC22×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC23×C8×C61C4
socleC23×C61C2×C42
prime radicalC24×D61C2×C4
cosocleC2×C4×D61C24
hypercenterC23×C8#6923
hypocenterC61C2×#1729
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C8

2350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1103398);