Finite Group Databasebeta

#44530622

order31264
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC977 ⋊ #117

Subgroups

subgroupG/H
center, FrattiniC22C22×D977
commutatorC2×C977C22×C4
FittingC22⋊C4×C977C2
socle, cosocleC22×C977C23
prime radicalC23×C977C22
hypercenterC22⋊C4D977
hypocenterC977#117
LCSG ▷ C2×C977 ▷ C977
UCSC1 ◁ C22 ◁ C22⋊C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15632

Polycyclic presentation:

2^5,977|a^2=e,c^2=d,b^a=bd,f^c=f^976

Conjugacy classes & character table

4900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31264, 102);