Finite Group DatabasebetaFinite Group Databasebeta| order | 15632 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C977 ⋊ C2 |
| Sylow | C977 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D977 |
| commutator, socle, cosocle | C2×C977 | C23 |
| Fitting | Q8×C977 | C2 |
| hypercenter | Q8 | D977 |
| hypocenter | C977 | #41 |
| LCS | G ▷ C2×C977 ▷ C977 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7816 |
Polycyclic presentation:
2^4,977|c^2=d,b^a=bd,e^a=e^976,e^b=e^976,e^c=e^9762450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44530687, #44530689, #44530693, … |
| maximal normal subgroup of | #44530687, #44530689, #44530693, … |
| maximal quotient of | #44530624, #44530628, Q8×Dic977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15632, 41);