Finite Group Databasebeta

C2×#21444204 #29646379

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#21444204

Splittings

FittingC22×C4⋊C8×C61 ⋊ C2
SylowC61 ⋊ C2×#1477

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC4×C61C23×C8
FrattiniC42C23×D61
FittingC22×C4⋊C8×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758222C4
cosocleC42×C61C24
hypercenterC22×C4⋊C8D61
hypocenterC61C2×#1477
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4⋊C8

1370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 135934);