Finite Group Databasebeta

Q8×#13063236 #25095266

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#13063236

Splittings

SylowC43 ⋊ Q8×#97

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC42×Q8×C43C2
socle, prime radicalC23×C43C23×C4
cosocleC22×C4×C43C24
hypercenterC42×Q8D43
hypocenterC43Q8×#97
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C42×Q8

954 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168237);