Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4⋊Q8×C239 ⋊ C2 |
| Sylow | C239 ⋊ #555 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D239 |
| commutator, socle, cosocle | C22×C239 | C24 |
| Fitting | C4⋊Q8×C239 | C2 |
| hypercenter | C4⋊Q8 | D239 |
| hypocenter | C239 | #555 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|b^2=f,c^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^238,d^b=de,g^b=g^238,g^c=g^2381691 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483629, #44483632, #44483691, … |
| maximal normal subgroup of | #44483629, #44483632, #44483691, … |
| maximal quotient of | #44487432, #44487499, #44487585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1265);