Finite Group Databasebeta

#44542230

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

Aliases

No aliases for this group.

Splittings

SylowC997 ⋊ C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D997
commutatorC2×C997C2×C8
FittingC2×C8×C997C2
socle, prime radicalC22×C997C2×C4
cosocleC2×C4×C997C22
hypercenterC2×C8D997
hypocenterC997C4⋊C8
LCSG ▷ C2×C997 ▷ C997
UCSC1 ◁ C2×C4 ◁ C2×C8

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31904

Polycyclic presentation:

2^5,997|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=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, 75);