Finite Group DatabasebetaFinite Group Databasebeta| order | 26508 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C472⋊C3 ⋊ C4 |
| Sylow | C472 ⋊ Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #27210411 |
| commutator, hypocenter | C472⋊C3 | C4 |
| Fitting, socle | C2×C472 | D3 |
| prime radical, cosocle | C2×C472⋊C3 | C2 |
| LCS | G ▷ C472⋊C3 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 564 |
Polycyclic presentation:
2,3,47^2,2|a^2=e,b^a=b^2,d^a=c^2d^46,c^b=c^20d^3,d^b=c^32d^26880 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26508, 12);