Finite Group Databasebeta

C2×#21461589 #30614130

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#21461589

Splittings

FittingC2×C4×D4×C61 ⋊ C4
SylowC61 ⋊ C2×#1762

Subgroups

subgroupG/H
centerC23C2×C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenterC2×C4×D4#6923
hypocenterC61C2×#1762
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1103685);