Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D16×C239 ⋊ C2 |
| Sylow | C239 ⋊ D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #21439901 |
| commutator, cosocle | C16×C239 | C22 |
| Frattini | C16 | C2×D239 |
| Fitting | D16×C239 | C2 |
| socle | C2×C239 | D16 |
| hypercenter | D16 | D239 |
| hypocenter | C239 | D32 |
| LCS | G ▷ C16×C239 ▷ C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^2381328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D32×D239, C2×#29504607, #44486855, … |
| maximal normal subgroup of | D32×D239, C2×#29504607, #44486855, … |
| maximal quotient of | #44482725, #44482726, #44482747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 384);