Finite Group Databasebeta

C8×D4×#6923 #30614429

order15616
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC8×D4×#6923

Splittings

FittingC8×D4×C61 ⋊ C4
SylowC61 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC2×C8C22×#6923
commutatorC2×C61C22×C4×C8
FrattiniC2×C4C23×#6923
FittingC8×D4×C61C4
socleC22×C61C22×C42
prime radicalC2×D4×D61C2×C4
cosocleC2×C4×D61C24
hypercenterC8×D4#6923
hypocenterC61C4×C8×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C8×D4

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1103984);