Finite Group DatabasebetaFinite Group Databasebeta| order | 16448 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C257 ⋊ C2 |
| Sylow | C257 ⋊ #537 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D257 |
| commutator, socle, cosocle | C22×C257 | C24 |
| Fitting | C2×C4⋊C4×C257 | C2 |
| hypercenter | C2×C4⋊C4 | D257 |
| hypocenter | C257 | #537 |
| LCS | G ▷ C22×C257 ▷ C257 | |
| UCS | C1 ◁ C22 ◁ C2×C4⋊C4 | |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8224 |
Polycyclic presentation:
2^6,257|d^2=e,b^a=be,c^a=cf,d^a=de,g^a=g^256,c^b=ce,g^c=g^2562582 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45663254, #45663257, #45663288, … |
| maximal normal subgroup of | #45663254, #45663257, #45663288, … |
| maximal quotient of | #45666913, #45666938, #45667003, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16448, 1130);