Finite Group Databasebeta

C2×#21451737 #29846418

order15616
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21451737

Splittings

FittingC22×C22⋊Q8×C61 ⋊ C2
SylowC61 ⋊ C2×#2638

Subgroups

subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC22×C22⋊Q8×C61C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC22×C22⋊Q8D61
hypocenterC61C2×#2638
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

2958 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 335973);