Finite Group Databasebeta

C2×#21443831 #29590236

order15616
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21443831

Splittings

SylowC61 ⋊ C2×#1348

Subgroups

subgroupG/H
centerC23#14519698
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC2×C61×#467C2
socleC23×C61#102
prime radicalC24×C61D8
cosocleC22×C8×C61C23
hypercenterC2×#467D61
hypocenterC61C2×#1348
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

506 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1378 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 79791);