Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C541 ⋊ C2 |
| Sylow | C541 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D541 |
| commutator, socle | C2×C541 | C2×C16 |
| Fitting | C32×C541 | C2 |
| prime radical | C2×D541 | C16 |
| cosocle | C16×C541 | C22 |
| hypercenter | C32 | D541 |
| hypocenter | C541 | M64 |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C16 ◁ C32 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
Polycyclic presentation:
2^6,541|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^b=g^5408680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 382);