Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C52×C112 ⋊ D3 |
| derived, Hall | C52⋊(C112⋊C3) ⋊ C2 |
| Sylow | C112 ⋊ #3874 |
| Sylow | C52 ⋊ #10624391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52⋊(C112⋊C3) | C2 |
| Fitting, socle | C52×C112 | D3 |
| LCS | G ▷ C52⋊(C112⋊C3) | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 165 |
Polycyclic presentation:
2,3,5^2,11^2|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^7588 conjugacy classes — view the full character table.
| maximal subgroup of | #49137550, #49137575, #49137576, … |
| maximal normal subgroup of | #49137550, #49137575, #49137576, … |
| maximal quotient of | #49137292, C2×#31827688 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 172);