Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C22×#120×C71 ⋊ C2 |
| Sylow | C71 ⋊ #34980 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D71 |
| commutator, socle, cosocle | C23×C71 | C25 |
| Fitting | C22×#120×C71 | C2 |
| hypercenter | C22×#120 | D71 |
| hypocenter | C71 | #34980 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×#120 | |
7786 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|b^a=bf,c^a=cg,e^a=eh,c^b=ch,d^b=dh,i^b=i^702024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 342102);