Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊((C5⋊D5)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C3⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C2×C3)⋊((C5⋊D5)⋊C3) |
| unambiguous semidirect product | (C2×C3⋊(C5⋊D5))⋊C3 |
| Fitting, socle | C2×C3×C52 ⋊ C2×C3 |
| derived | C3×C52 ⋊ C22×C3 |
| Hall | C3×C52⋊C3 ⋊ C22 |
| Sylow | C52 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊((C5⋊D5)⋊C3) |
| commutator, cosocle, hypocenter | C3×C52 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C2×C3 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 90 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | #14268155, #14268156, #14268157, … |
| maximal normal subgroup of | #14268155, #14268156, #14268157, … |
| maximal quotient of | #10597155⋊C3, C4×C3⋊((C5⋊D5)⋊C3), C4⋊(C3⋊((C5⋊D5)⋊C3)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 103);