Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C42 |
No aliases for this group.
| Fitting | C4×#95×C71 ⋊ C2 |
| Sylow | C71 ⋊ #15142 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D71 |
| commutator, socle, cosocle | C24×C71 | C24 |
| Fitting | C4×#95×C71 | C2 |
| hypercenter | C4×#95 | D71 |
| hypocenter | C71 | #15142 |
| LCS | G ▷ C24×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
4382 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 4382 conjugacy classes of subgroups — too many to draw. Only its 515 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|b^2=e,c^2=f,d^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^70,c^b=cg2864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 106275);