Finite Group Databasebeta

C8×#13063350 #25066009

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC8×#13063350

Splittings

FittingC8×#41×C43 ⋊ C2
SylowC43 ⋊ C8×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D43
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC8×#41×C43C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063350C4
cosocleC42×C43C24
hypercenterC8×#41D43
hypocenterC43C8×AGL(1,ℤ/8)
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C8×#41

802 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 138980);