Finite Group DatabasebetaFinite Group Databasebeta| order | 14624 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C457 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D457 |
| commutator, hypocenter | C457 | C32 |
| Fitting, cosocle | C16×C457 | C2 |
| socle, prime radical | C2×C457 | C16 |
| LCS | G ▷ C457 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14624 |
Polycyclic presentation:
2^5,457|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^4563680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D457, C2×#28410458, #44416610, … |
| maximal normal subgroup of | C32×D457, C2×#28410458, #44416610, … |
| maximal quotient of | #44416496, C2×#28410458 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14624, 52);