Finite Group Databasebeta

#44529979

order31184
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1949 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D1949
commutator, cosocleC4×C1949C22
FrattiniC4C2×D1949
Fitting, prime radicalD4×C1949C2
socleC2×C1949D4
hypercenterD4D1949
hypocenterC1949SD16
LCSG ▷ C4×C1949 ▷ C2×C1949 ▷ C1949
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15592

Polycyclic presentation:

2^4,1949|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1948,c^b=cd

Conjugacy classes & character table

4877 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31184, 28);