Finite Group Databasebeta

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Q8×#13063245 #25113182

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

Aliases

direct productQ8×#13063245

Splittings

FittingQ8×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ Q8×#102

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingQ8×C4⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterQ8×C4⋊C4D43
hypocenterC43Q8×#102
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ Q8×C4⋊C4

1314 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 186153);