Finite Group DatabasebetaFinite Group Databasebeta| order | 36100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#31825265 |
| derived, Hall | C192⋊C25 ⋊ C22 |
| Sylow | C192 ⋊ C2×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #31825265 |
| commutator, cosocle, hypocenter | C192⋊C25 | C22 |
| Frattini | C5 | C2×#16813380 |
| Fitting, socle | C2×C5×C192 | D5 |
| LCS | G ▷ C192⋊C25 | |
| UCS | C1 ◁ C2 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 950 |
442 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36100, 50);