Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D4×C239 ⋊ C2 |
| Sylow | C239 ⋊ #550 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D239 |
| commutator, socle, cosocle | C22×C239 | C24 |
| Fitting | C4×D4×C239 | C2 |
| hypercenter | C4×D4 | D239 |
| hypocenter | C239 | #550 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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,d^2=e,b^a=be,c^a=cf,d^b=de,g^b=g^2382405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483612, #44483616, #44483674, … |
| maximal normal subgroup of | #44483612, #44483616, #44483674, … |
| maximal quotient of | #44487388, C4⋊C4×Dic478, #44487493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1220);