Finite Group Databasebeta

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Q8×C22⋊(C43⋊C8) #25113113

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×C22⋊(C43⋊C8)

Splittings

SylowC43 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C23×C8
FittingC22×C4×Q8×C43C2
socleC23×C43C23×C4
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC22×C4×Q8D43
hypocenterC43Q8×C22⋊C8
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

1356 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, 186084);