Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C19 ⋊ M16 |
| Sylow | C19 ⋊ ΓL(1,𝔽25) |
| Sylow | C3 ⋊ #64520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D19 |
| commutator, socle | C2×C3×C19 | C2×C4 |
| Fitting, cosocle | C3×C4×C19 | C22 |
| prime radical | C2×D3×C19 | C4 |
| hypocenter | C3×C19 | M16 |
| LCS | G ▷ C2×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C4 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 456 |
Polycyclic presentation:
2^4,3,19|a^2=c,c^2=d,b^a=bd,f^a=f^18,e^b=e^2126 conjugacy classes — view the full character table.
| maximal subgroup of | D19×ΓL(1,𝔽25), #14269163, #14269182, … |
| maximal normal subgroup of | D19×ΓL(1,𝔽25), #14269163, #14269182, … |
| maximal quotient of | #14268843, (C2×D3)⋊(C19⋊C8), Dic3⋊(C19⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 27);