Finite Group DatabasebetaFinite Group Databasebeta| order | 30108 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C193 ⋊ C3×C4 |
| Hall | #23756690 ⋊ C3 |
| Hall | #21419088 ⋊ C4 |
| Sylow | C193 ⋊ Dic13⋊C3 |
| Sylow | C13 ⋊ #11715871⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C193 | C3×C4 |
| prime radical | #28418818 | C2 |
| cosocle | C13×D193 | C2×C3 |
| LCS | G ▷ C13×C193 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2509 |
Polycyclic presentation:
2,3,2,13,193|a^2=c,d^a=d^12,e^a=e^81,d^b=d^3,e^b=e^84,e^c=e^192224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30108, 39);