Finite Group Databasebeta

C2×C4×#14519746 #29838427

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

Aliases

direct productC2×C4×#14519746

Splittings

FittingC25×C4×C61 ⋊ C2
SylowC61 ⋊ C2×C4×#120

Subgroups

subgroupG/H
centerC23×C4C22×D61
commutatorC22×C61C24×C4
FrattiniC23C24×D61
FittingC25×C4×C61C2
socleC24×C61C24
prime radicalC22×#14519746C2
cosocleC23×C61C25
hypercenterC25×C4D61
hypocenterC61C2×C4×#120
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23×C4 ◁ C25×C4

8582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

3952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 327982);