Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #125×C239 ⋊ C2 |
| Sylow | C239 ⋊ #562 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D239 |
| commutator, socle, cosocle | C22×C239 | C24 |
| Fitting | #125×C239 | C2 |
| hypercenter | #125 | D239 |
| hypocenter | C239 | #562 |
| LCS | G ▷ C22×C239 ▷ C239 | |
| UCS | C1 ◁ C22 ◁ #125 | |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|c^2=e,b^a=be,c^a=cf,d^a=def,g^a=g^238,c^b=cef,d^b=de,g^b=g^238,g^c=g^238,g^d=g^2381685 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483840, #44483843, #44483863, … |
| maximal normal subgroup of | #44483840, #44483843, #44483863, … |
| maximal quotient of | #44487693, #44487703, #44487713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1297);