Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C52×C41 ⋊ Dic3 |
| derived, Hall | C41×C52⋊C3 ⋊ C4 |
| Hall | C52⋊C3 ⋊ #4223 |
| Sylow | C41 ⋊ #64470 |
| Sylow | C52 ⋊ C3⋊#4223 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C41×C52⋊C3 | C4 |
| Fitting, socle | C52×C41 | Dic3 |
| prime radical, cosocle | C52⋊C3×D41 | C2 |
| LCS | G ▷ C41×C52⋊C3 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,41,5^2|a^2=b,c^a=c^2,d^a=d^32,e^a=e^2f,f^a=e^2f^3,d^b=d^40,e^c=e^2f^4,f^c=e^2f^2136 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#27134237, C3⋊#27134237 |
| maximal normal subgroup of | C3×#27134237 |
| maximal quotient of | #49146798, C3×#27134237, C3⋊#27134237 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 99);