Finite Group DatabasebetaFinite Group Databasebeta| order | 37792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C1181 ⋊ C2 |
| Sylow | C1181 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D1181 |
| commutator, socle, cosocle | C22×C1181 | C23 |
| Fitting | C24×C1181 | C2 |
| hypercenter | C24 | D1181 |
| hypocenter | C1181 | #120 |
| LCS | G ▷ C22×C1181 ▷ C1181 | |
| UCS | C1 ◁ C22 ◁ C24 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9448 |
Polycyclic presentation:
2^5,1181|b^a=bd,c^a=ce,f^a=f^11809454 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37792, 115);