Finite Group DatabasebetaFinite Group Databasebeta| order | 36700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C367 · Schur multiplier (H2) = C1 |
| direct product | #1042×C367 |
| Fitting, socle, Hall | C52×C367 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C367 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C367 | #1042 |
| commutator, hypocenter | C52 | C4×C367 |
| Frattini | C1 | G |
| Fitting, socle | C52×C367 | C4 |
| prime radical | C5×D5×C367 | C2 |
| cosocle | C5×D5 | C2×C367 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C367 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7340 |
4771 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36700, 22);