Finite Group DatabasebetaFinite Group Databasebeta| order | 32624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C2039 ⋊ C2 |
| Sylow | C2039 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D2039 |
| commutator, socle | C2×C2039 | C2×C4 |
| Fitting | C8×C2039 | C2 |
| prime radical | C2×D2039 | C4 |
| cosocle | C4×C2039 | C22 |
| hypercenter | C8 | D2039 |
| hypocenter | C2039 | M16 |
| LCS | G ▷ C2×C2039 ▷ C2039 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16312 |
Polycyclic presentation:
2^4,2039|a^2=c,c^2=d,b^a=bd,e^b=e^20388162 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32624, 23);