Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C4×C19 ⋊ C2 |
| Hall | C3×C19 ⋊ #41 |
| Sylow | C19 ⋊ #235 |
| Sylow | C3 ⋊ #64541 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D57 |
| commutator, socle, cosocle | C2×C3×C19 | C23 |
| Frattini | C2 | C22×D57 |
| Fitting | C2×C3×C4×C19 | C2 |
| hypercenter | C2×C4 | D57 |
| hypocenter | C3×C19 | #41 |
| LCS | G ▷ C2×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 456 |
Polycyclic presentation:
2^4,3,19|b^2=d,c^a=cd,e^a=e^2,f^a=f^18234 conjugacy classes — view the full character table.
| maximal subgroup of | #14268870, #14268871, #14268999, … |
| maximal normal subgroup of | #14268870, #14268871, #14268999, … |
| maximal quotient of | C4×Dic114, #14269708, #14269710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 196);