Finite Group DatabasebetaFinite Group Databasebeta| order | 24843 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C72×C169 ⋊ C3 |
| Sylow | C169 ⋊ #3861 |
| Sylow | C72 ⋊ C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C72×C169 | C3 |
| Frattini | C13 | #14274263 |
| socle | C72×C13 | C13⋊C3 |
| LCS | G ▷ C72×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8281 |
Polycyclic presentation:
3,7^2,13^2|d^13=e^6,b^a=b^2,c^a=c^2,d^a=d^3e,e^a=e^32763 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24843, 13);