Finite Group DatabasebetaFinite Group Databasebeta| order | 26900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C25×C269 ⋊ C4 |
| Sylow | C269 ⋊ Dic25 |
| Sylow | C25 ⋊ #11761640 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C25×C269 | C4 |
| Frattini | C5 | #19129043 |
| socle | C5×C269 | Dic5 |
| prime radical | C5×D269 | D5 |
| cosocle | C25×D269 | C2 |
| LCS | G ▷ C25×C269 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6725 |
Polycyclic presentation:
2^2,5,269,5|a^2=b,c^5=e^4,c^a=c^4e,d^a=d^82,e^a=e^4,d^b=d^2681703 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26900, 11);