Finite Group Databasebeta

#44570270

order32464
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC2029 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D2029
commutator, cosocleC4×C2029C22
FrattiniC4C2×D2029
Fitting, prime radicalD4×C2029C2
socleC2×C2029D4
hypercenterD4D2029
hypocenterC2029SD16
LCSG ▷ C4×C2029 ▷ C2×C2029 ▷ C2029
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16232

Polycyclic presentation:

2^4,2029|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2028,c^b=cd

Conjugacy classes & character table

5077 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32464, 28);