Finite Group DatabasebetaFinite Group Databasebeta| order | 912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | #64545 ⋊ C3 |
| Sylow | C19 ⋊ #41⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4×D19 |
| commutator, Fitting, cosocle, hypocenter | Q8×C19 | C2×C3 |
| socle | C2×C19 | C2×A4 |
| LCS | G ▷ Q8×C19 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2,3,2^2,19,2|a^2=f,c^2=f,d^2=f,e^a=e^18,c^b=cd,d^b=c,d^c=df77 conjugacy classes — view the full character table.
| maximal subgroup of | #14269816, #14269817, #14269818, … |
| maximal normal subgroup of | #14269816, #14269817, #14269818, … |
| maximal quotient of | SL(2,𝔽3)×Dic19, C2×#11744919 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 130);