Finite Group Databasebeta

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Q8×#13063283 #25256022

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productQ8×#13063283

Splittings

FittingQ8×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ Q8×#117

Subgroups

subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingQ8×C4⋊C4×C43C2
socle, cosocleC23×C43C25
prime radicalC23×D43C24
hypercenterQ8×C4⋊C4D43
hypocenterC43Q8×#117
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

2434 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328993);