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 | D19⋊A4 |
| 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=d,d^b=cdf,e^b=e^7,d^c=df29 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11744922, #14269884, #14269885, … |
| maximal normal subgroup of | C2×#11744922, #14269884, #14269885, … |
| maximal quotient of | Dic19⋊SL(2,𝔽3), C2×#11744922 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(912, 133);