Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of #90646 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#90646 |
| derived, Hall | C52⋊C9 ⋊ C22 |
| Sylow | C52 ⋊ C2×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #90646 |
| commutator, cosocle, hypocenter | C52⋊C9 | C22 |
| Frattini | C3 | C2×#3874 |
| Fitting, socle | C2×C3×C52 | D3 |
| LCS | G ▷ C52⋊C9 | |
| UCS | C1 ◁ C2 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | #14267935, #14267936, #14267938, … |
| maximal normal subgroup of | #14267935, #14267936, #14267938, … |
| maximal quotient of | #14267939, C4×#90646, C4⋊#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 49);