Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4⋊Q8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #536 |
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^238,c^b=ce,g^d=g^2381688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44486236, #44486241 |
| maximal normal subgroup of | #44486236, #44486241 |
| maximal quotient of | #44487131, #44487139, #44487169, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1124);