Finite Group Databasebeta

#38736451

order25029
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C32

Aliases

No aliases for this group.

Splittings

SylowC103 ⋊ #6868

Subgroups

subgroupG/H
centerC32C32⋊(C103⋊C3)
commutatorC32×C103C3×C9
FrattiniC33C3×C103⋊C3
FittingC32×C9×C103C3
socleC32×C103H(3,𝔽3)
prime radical, cosocleC33×C103C32
hypercenterC32×C9C103⋊C3
hypocenterC103#6868
LCSG ▷ C32×C103 ▷ C3×C103 ▷ C103
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8343

Polycyclic presentation:

3^5,103|a^3=d,b^3=e^2,b^a=bc,c^a=ce,f^a=f^56

Conjugacy classes & character table

2805 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25029, 100);