Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #386×C137 ⋊ C2 |
| Sylow | C137 ⋊ #2403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D137 |
| commutator, socle, cosocle | C23×C137 | C24 |
| Fitting | #386×C137 | C2 |
| hypercenter | #386 | D137 |
| hypocenter | C137 | #2403 |
| LCS | G ▷ C23×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ #386 | |
1564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^136,h^c=h^1361942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 7822);