Finite Group Databasebeta

#44526048

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

Aliases

No aliases for this group.

Splittings

SylowC967 ⋊ #104

Subgroups

subgroupG/H
centerC4C22⋊D967
commutatorC4×C967C2×C4
FrattiniC2×C4C2×D967
Fitting, prime radical#41×C967C2
socleC2×C967C22⋊C4
cosocleC2×C4×C967C22
hypercenter#41D967
hypocenterC967#104
LCSG ▷ C4×C967 ▷ C2×C967 ▷ C967
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7736

Polycyclic presentation:

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

Conjugacy classes & character table

4844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 73);