Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C541 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #14524194 |
| commutator, hypocenter | C541 | C4×C16 |
| Frattini | C2×C4 | C2×#14524194 |
| Fitting | C2×C8×C541 | C4 |
| socle, prime radical | C22×C541 | C2×C8 |
| cosocle | C2×#16864513 | C22 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34624 |
Polycyclic presentation:
2^6,541|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^52,g^b=g^540,g^c=g^5402224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1435);