Finite Group Databasebeta

C4×Q8×C22⋊D73 #33245846

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

Aliases

direct productC4×Q8×C22⋊D73

Splittings

FittingC22×C4×Q8×C73 ⋊ C2
SylowC73 ⋊ C4×D4×Q8

Subgroups

subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC22×C4×Q8×C73C2
socle, cosocleC23×C73C25
prime radicalC22×C22⋊D73C23
hypercenterC22×C4×Q8D73
hypocenterC73C4×D4×Q8
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

3148 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, 329430);