Finite Group Databasebeta

Q8×C22⋊#10596831 #33102500

order18688
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productQ8×C22⋊#10596831

Splittings

SylowC73 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D73
commutatorC22×C73C23×C8
FittingC22×C4×Q8×C73C2
socleC23×C73C23×C4
prime radicalC24×C73C22×C4
cosocleC22×C4×C73C24
hypercenterC22×C4×Q8D73
hypocenterC73Q8×C22⋊C8
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 186084);