Finite Group Databasebeta

#45686753

order33328
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC2083 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D2083
commutator, cosocleC4×C2083C22
FrattiniC4C2×D2083
Fitting, prime radicalD4×C2083C2
socleC2×C2083D4
hypercenterD4D2083
hypocenterC2083SD16
LCSG ▷ C4×C2083 ▷ C2×C2083 ▷ C2083
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16664

Polycyclic presentation:

2^4,2083|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2082,c^b=cd

Conjugacy classes & character table

5212 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33328, 28);