Finite Group DatabasebetaFinite Group Databasebeta| order | 26508 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C47 |
No aliases for this group.
| Fitting, socle, Sylow | C472 ⋊ Dic3 |
| derived, Hall | C472⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C472⋊C3 | C4 |
| Fitting, socle | C472 | Dic3 |
| prime radical, cosocle | (C47⋊D47)⋊C3 | C2 |
| LCS | G ▷ C472⋊C3 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 282 |
Polycyclic presentation:
2^2,3,47^2|a^2=b,c^a=c^2,d^a=d^22e^29,e^a=d^40e^25,d^b=d^46,e^b=e^46,d^c=d^37e^11,e^c=d^43e^9190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26508, 21);