Finite Group Databasebeta

#44526077

order30944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC967 ⋊ #117

Subgroups

subgroupG/H
center, FrattiniC22C22×D967
commutatorC2×C967C22×C4
FittingC22⋊C4×C967C2
socle, cosocleC22×C967C23
prime radicalC23×C967C22
hypercenterC22⋊C4D967
hypocenterC967#117
LCSG ▷ C2×C967 ▷ C967
UCSC1 ◁ C22 ◁ C22⋊C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15472

Polycyclic presentation:

2^5,967|a^2=e,c^2=d,b^a=bd,f^c=f^966

Conjugacy classes & character table

4850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 102);