Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C41×C52⋊C3 ⋊ C4 |
| Hall | C52×C41 ⋊ Dic3 |
| Hall | C52⋊C3 ⋊ Dic41 |
| Sylow | C41 ⋊ #64470 |
| Sylow | C52 ⋊ Dic123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C41⋊#3874 |
| commutator, hypocenter | C41×C52⋊C3 | C4 |
| Fitting, socle | C2×C52×C41 | D3 |
| prime radical, cosocle | C2×C41×C52⋊C3 | C2 |
| LCS | G ▷ C41×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,41,5^2,2|a^2=f,b^a=b^2,c^a=c^40,d^a=d^2e,e^a=d^2e^3,d^b=d^2e^4,e^b=d^2e^2466 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#27134196, C3⋊#27134196 |
| maximal normal subgroup of | C3×#27134196 |
| maximal quotient of | #49146675, C3×#27134196, C3⋊#27134196 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 58);