Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C71 ⋊ C4⋊#401 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D71 |
| commutator, socle, prime radical, cosocle | C24×C71 | C24 |
| Fitting | C2×#401×C71 | C2 |
| hypercenter | C2×#401 | D71 |
| hypocenter | C71 | C4⋊#401 |
| LCS | G ▷ C24×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C2×#401 | |
1106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18176 |
Polycyclic presentation:
2^8,71|a^2=efg,b^2=ef,c^2=e,d^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,i^d=i^701604 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 106362);