Finite Group DatabasebetaFinite Group Databasebeta| order | 38100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #1042×C127⋊C3 |
| unambiguous semidirect product | (#1042×C127)⋊C3 |
| Fitting, socle, derived, Hall | C52×C127 ⋊ C3×C4 |
| Hall | #1042×C127 ⋊ C3 |
| Hall | C52×C127⋊C3 ⋊ C4 |
| Sylow | C127 ⋊ C3×#1042 |
| Sylow | C52 ⋊ C4×C127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C127 | C3×C4 |
| prime radical | C5×D5×C127⋊C3 | C2 |
| cosocle | C5×D5×C127 | C2×C3 |
| LCS | G ▷ C52×C127 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2540 |
585 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38100, 86);