Finite Group Databasebeta

C2×C8×#11758190 #29649378

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C8×#11758190

Splittings

FittingC2×C82×C61 ⋊ C2
SylowC61 ⋊ C2×C8×SD16

Subgroups

subgroupG/H
centerC22×C8D244
commutatorC4×C61C23×C8
FrattiniC42C23×D61
FittingC2×C82×C61C2
socleC23×C61C4×D4
prime radicalC22×D244C2×C4
cosocleC42×C61C24
hypercenterC2×C82D61
hypocenterC61C2×C8×SD16
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C82

822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

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, 138933);