Finite Group DatabasebetaFinite Group Databasebeta| order | 15225 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52×C7 · Schur multiplier (H2) = C5 |
| Fitting, socle, Hall | C3×C52×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C3×C52×C7 |
| Hall | C52×C29 ⋊ C3×C7 |
| Hall | C3×C29 ⋊ C52×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C3×C52×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C3×C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2175 |
825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C52×D29⋊C7, C3×C5×C5⋊(D29⋊C7), C3×C5×D5×C29⋊C7, … |
| maximal normal subgroup of | C3×C52×D29⋊C7, C3×C5×C5⋊(D29⋊C7), C3×C5×D5×C29⋊C7, … |
| maximal quotient of | C2×C3×C52×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15225, 6);