Finite Group Databasebeta

C2×#21446276 #29681799

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#21446276

Splittings

FittingC2×C61×#342 ⋊ C2
SylowC61 ⋊ C2×#1899

Subgroups

subgroupG/H
centerC23C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC2×C61×#342C2
socleC23×C61C2×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC24×C61C24
hypercenterC2×#342D61
hypocenterC61C2×#1899
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

2066 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 171354);