Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of #64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C5 |
| direct product | C41×#64480 |
| Fitting, socle, Hall | C52×C41 ⋊ Dic3 |
| derived, Hall | C52⋊C3 ⋊ C4×C41 |
| Hall | C41×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ Dic3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #64480 |
| commutator, hypocenter | C52⋊C3 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C52×C41 | Dic3 |
| prime radical | C41×(C5⋊D5)⋊C3 | C2 |
| cosocle | (C5⋊D5)⋊C3 | C2×C41 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C41 | |
36 conjugacy classes of subgroups.
328 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C41×#64480, C41×C3⋊#64480 |
| maximal normal subgroup of | C3×C41×#64480 |
| maximal quotient of | C41×#11744634, C3×C41×#64480, C41×C3⋊#64480 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 105);