Finite Group Databasebeta

C2×#21444200 #29646364

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

Aliases

direct productC2×#21444200

Splittings

FittingC2×C61×Q8⋊C8 ⋊ C2
SylowC61 ⋊ C2×#1476

Subgroups

subgroupG/H
centerC22×C4D4×D61
commutatorC4×C61C23×C8
FrattiniC42C23×D61
FittingC2×C61×Q8⋊C8C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758226C4
cosocleC42×C61C24
hypercenterC2×Q8⋊C8D61
hypocenterC61C2×#1476
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

1430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 135919);