Finite Group DatabasebetaFinite Group Databasebeta| order | 1911 |
| isoclinism | isoclinic class of #14274262 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C13 ⋊ C3 |
| Sylow | C72 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ #3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13 | C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 637 |
Polycyclic presentation:
3,7^2,13|b^a=b^4,c^a=c^4,d^a=d^3215 conjugacy classes — view the full character table.
| maximal subgroup of | #16838447, #16838449, #16838457, … |
| maximal normal subgroup of | #16838447, #16838449, #16838457, … |
| maximal quotient of | C2×#14274262, C11×#14274262, #38732967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1911, 11);