Finite Group DatabasebetaFinite Group Databasebeta| order | 11912 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1489 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #20238494 |
| commutator, hypocenter | C1489 | C8 |
| Fitting, socle, prime radical | C2×C1489 | C4 |
| cosocle | Dic1489 | C2 |
| LCS | G ▷ C1489 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1489|a^2=b,b^2=c,d^a=d^225,d^b=d^1488752 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#26045522, #37558500, #37558501, … |
| maximal normal subgroup of | C2×#26045522, #37558500, #37558501, … |
| maximal quotient of | #37558495, C2×#26045522 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11912, 13);