Finite Group Databasebeta

C2×D4×#11758190 #30555231

order15616
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×D4×#11758190

Splittings

FittingC2×C8×D4×C61 ⋊ C2
SylowC61 ⋊ C2×D4×SD16

Subgroups

subgroupG/H
centerC23C22×D244
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C8×D4×C61C2
socleC23×C61C22×D4
prime radicalC2×D4×D244C2
hypercenterC2×C8×D4D61
hypocenterC61C2×D4×SD16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

3226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1044786);