Finite Group Databasebeta

Q8×#13063240 #25113146

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ8×#13063240

Splittings

SylowC43 ⋊ Q8×#99

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×D4×Q8×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D4×C43C23
cosocleC24×C43C24
hypercenterC2×D4×Q8D43
hypocenterC43Q8×#99
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C2×D4×Q8

1354 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 186117);