Finite Group Databasebeta

#44542241

order31904
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC997 ⋊ M32

Subgroups

subgroupG/H
center, FrattiniC8C2×D997
commutator, socleC2×C997C2×C8
FittingC2×C8×C997C2
prime radicalC22×C997C8
cosocleC8×C997C22
hypercenterC2×C8D997
hypocenterC997M32
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C8 ◁ C2×C8

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15952

Polycyclic presentation:

2^5,997|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^996

Conjugacy classes & character table

7988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31904, 86);