Finite Group Databasebeta

#44526080

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

Aliases

No aliases for this group.

Splittings

SylowC967 ⋊ #117

Subgroups

subgroupG/H
centerC2×C4C2×D967
commutatorC2×C967C22×C4
FrattiniC22C22×D967
FittingC22×C4×C967C2
socle, cosocleC22×C967C23
prime radicalC23×C967C22
hypercenterC22×C4D967
hypocenterC967#117
LCSG ▷ C2×C967 ▷ C967
UCSC1 ◁ C2×C4 ◁ 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^a=f^966

Conjugacy classes & character table

7748 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 105);