Finite Group DatabasebetaFinite Group Databasebeta| order | 24548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
No aliases for this group.
| Fitting, socle, derived, Hall | C17×C192 ⋊ C4 |
| Sylow | C192 ⋊ #595 |
| Sylow | C17 ⋊ #13089659 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C192 | C4 |
| prime radical, cosocle | C17⋊(C19⋊D19) | C2 |
| LCS | G ▷ C17×C192 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 646 |
Polycyclic presentation:
2^2,17,19^2|a^2=b,c^a=c^13,d^a=d^12e^14,e^a=d^10e^7,c^b=c^16,d^b=d^18,e^b=e^181538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24548, 21);