Finite Group DatabasebetaFinite Group Databasebeta| order | 23076 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C641 ⋊ C4 |
| Sylow | C641 ⋊ #157 |
| Sylow | C32 ⋊ Dic641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C641 | C4 |
| prime radical, cosocle | C3⋊D3×C641 | C2 |
| LCS | G ▷ C32×C641 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3846 |
Polycyclic presentation:
2^2,3^2,641|a^2=b,c^a=cd,d^a=cd^2,e^a=e^640,c^b=c^2,d^b=d^21926 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23076, 22);