Finite Group Databasebeta

#37524024

order22928
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1433 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D1433
commutator, cosocleC4×C1433C22
FrattiniC4C2×D1433
Fitting, prime radicalD4×C1433C2
socleC2×C1433D4
hypercenterD4D1433
hypocenterC1433SD16
LCSG ▷ C4×C1433 ▷ C2×C1433 ▷ C1433
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11464

Polycyclic presentation:

2^4,1433|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1432,c^b=cd

Conjugacy classes & character table

3587 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22928, 28);