Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C39 |
No aliases for this group.
| Fitting | C37×3−1+4 ⋊ C3 |
| Sylow | C37 ⋊ #10624943 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C34×C37⋊C3 |
| commutator, socle, cosocle | C3×C37 | C35 |
| Fitting | C37×3−1+4 | C3 |
| prime radical | C37⋊H(5,𝔽3) | C3 |
| hypercenter | 3−1+4 | C37⋊C3 |
| hypocenter | C37 | #10624943 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3 ◁ 3−1+4 | |
5490 conjugacy classes of subgroups; only the 2878 normal subgroups are shown.
This group has 5490 conjugacy classes of subgroups — too many to draw. Only its 2878 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2997 |
Polycyclic presentation:
3^6,37|e^3=f,b^a=bf,d^a=df,g^a=g^10,c^b=cf,g^e=g^261245 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 4032);