Finite Group DatabasebetaFinite Group Databasebeta| order | 14368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C449 ⋊ C2 |
| Sylow | C449 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D449 |
| commutator, socle, cosocle | C22×C449 | C23 |
| Fitting | C24×C449 | C2 |
| hypercenter | C24 | D449 |
| hypocenter | C449 | #120 |
| LCS | G ▷ C22×C449 ▷ C449 | |
| UCS | C1 ◁ C22 ◁ C24 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3592 |
Polycyclic presentation:
2^5,449|b^a=bd,c^a=ce,f^a=f^4483598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43272193, #120×D449, C2×#28385309, … |
| maximal normal subgroup of | #43272193, #120×D449, C2×#28385309, … |
| maximal quotient of | #43271863, #43271880, #43271886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14368, 115);