Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52⋊(C112⋊C3) ⋊ C4 |
| Hall | C52×C112 ⋊ Dic3 |
| Sylow | C112 ⋊ #64470 |
| Sylow | C52 ⋊ #13089712 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31827688 |
| commutator, hypocenter | C52⋊(C112⋊C3) | C4 |
| Fitting, socle | C2×C52×C112 | D3 |
| prime radical, cosocle | C2×C52⋊(C112⋊C3) | C2 |
| LCS | G ▷ C52⋊(C112⋊C3) | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 660 |
Polycyclic presentation:
2,3,5^2,11^2,2|a^2=g,b^a=b^2,d^a=cd^4,f^a=e^4f^10,c^b=c^3d^3,d^b=c^4d,e^b=e^3f,f^b=e^9f^71176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 428);