Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11 |
| direct product | D5×C5⋊((C11⋊D11)⋊C3) |
| unambiguous semidirect product | (C5×D5)⋊((C11⋊D11)⋊C3) |
| unambiguous semidirect product | (D5×C5⋊(C11⋊D11))⋊C3 |
| Fitting, socle, derived, Hall | C52×C112 ⋊ C22×C3 |
| Hall | D5×C5⋊(C11⋊D11) ⋊ C3 |
| Hall | C52×C112⋊C3 ⋊ C22 |
| Hall | C112⋊C3 ⋊ D52 |
| Sylow | C112 ⋊ C3×D52 |
| Sylow | C52 ⋊ C2×(C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C112 | C22×C3 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
192 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 330 |
448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 742);