Finite Group Databasebeta

C4×C22⋊Q8×D73 #33244426

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×C22⋊Q8×D73

Splittings

FittingC4×C22⋊Q8×C73 ⋊ C2
SylowC73 ⋊ C2×C4×C22⋊Q8

Subgroups

subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC4×C22⋊Q8×C73C2
socle, cosocleC23×C73C25
prime radicalC24×D73C23
hypercenterC4×C22⋊Q8D73
hypocenterC73C2×C4×C22⋊Q8
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×C22⋊Q8

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 328010);