Finite Group Databasebeta

C8×#14519772 #29688228

order15616
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productC8×#14519772

Splittings

FittingC8×C4⋊C4×C61 ⋊ C2
SylowC61 ⋊ C8×#126

Subgroups

subgroupG/H
centerC22×C8C22×D61
commutatorC22×C61C23×C8
FrattiniC22×C4C23×D61
FittingC8×C4⋊C4×C61C2
socleC23×C61C23×C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenterC8×C4⋊C4D61
hypocenterC61C8×#126
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 177783);