Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C37 ⋊ C2 |
| Sylow | C37 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D37 |
| commutator, socle, cosocle | C22×C37 | C23 |
| Fitting | C4⋊C4×C37 | C2 |
| prime radical | C22×D37 | C22 |
| hypercenter | C4⋊C4 | D37 |
| hypocenter | C37 | #126 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^5,37|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^36,f^c=f^36194 conjugacy classes — view the full character table.
| maximal subgroup of | #126×D37, C2×#11924531, #14558060, … |
| maximal normal subgroup of | #126×D37, C2×#11924531, #14558060, … |
| maximal quotient of | #14557400, #14557414, #14557416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 141);