Finite Group Databasebeta

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Q8×C4⋊C4×D89 #36713726

order22784
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productQ8×C4⋊C4×D89

Splittings

FittingQ8×C4⋊C4×C89 ⋊ C2
SylowC89 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C24×D89
commutatorC22×C89C24×C4
FittingQ8×C4⋊C4×C89C2
socle, cosocleC23×C89C25
prime radicalC23×D89C24
hypercenterQ8×C4⋊C4D89
hypocenterC89C2×Q8×C4⋊C4
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11392

Conjugacy classes & character table

2300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 328866);