Finite Group Databasebeta

C8×#14519834 #30597411

order15616
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC8×#14519834

Splittings

SylowC61 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
centerC22×C8C2×#6923
commutatorC2×C61C2×C82
FrattiniC22×C4C22×#6923
FittingC2×C4×C8×C61C4
socleC23×C61C2×C42
prime radicalC23×D61C42
cosocleC2×C4×Dic61C23
hypercenterC2×C4×C8#6923
hypocenterC61C8×C22⋊C8
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C8 ◁ C2×C4×C8

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1086966);