Finite Group Databasebeta

D8×#11758189 #29651430

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD8×#11758189

Splittings

FittingC8×D8×C61 ⋊ C2
SylowC61 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC8×D8×C61C2
socleC22×C61C2×C4×D4
prime radicalC2×D8×D61C4
cosocleC42×C61C24
hypercenterC8×D8D61
hypocenterC61M16×D8
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 140985);