Finite Group Databasebeta

C2×#21448635 #29839181

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#21448635

Splittings

FittingC2×C61×#379 ⋊ C2
SylowC61 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC2×C61×#379C2
socleC24×C61C24
prime radicalC24×C22⋊D61C2
cosocleC23×C61C25
hypercenterC2×#379D61
hypocenterC61C2×D4×C22⋊C4
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#379

8774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 328736);