Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q16×C457 ⋊ C2 |
| Sylow | C457 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D457 |
| commutator, cosocle | C4×C457 | C23 |
| Frattini | C4 | C22×D457 |
| Fitting | Q16×C457 | C2 |
| socle | C2×C457 | C2×D4 |
| hypercenter | Q16 | D457 |
| hypocenter | C457 | #135 |
| LCS | G ▷ C4×C457 ▷ C2×C457 ▷ C457 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7312 |
Polycyclic presentation:
2^5,457|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^456,d^b=de,f^b=f^456,f^c=f^4561610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44417208, #44417210, #44417214, … |
| maximal normal subgroup of | #44417208, #44417210, #44417214, … |
| maximal quotient of | #44416772, #44416814, #44416859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 169);