Finite Group Databasebeta

C2×C4×#14519705 #29677724

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#14519705

Splittings

FittingC2×C43×C61 ⋊ C2
SylowC61 ⋊ C2×C4×#104

Subgroups

subgroupG/H
centerC2×C42D244
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC2×C43×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×C43D61
hypocenterC61C2×C4×#104
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C2×C43

1878 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, 167279);