Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C37 ⋊ C2 |
| Sylow | C37 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D37 |
| commutator, socle, cosocle | C2×C37 | C24 |
| Fitting | #41×C37 | C2 |
| hypercenter | #41 | D37 |
| hypocenter | C37 | H(5,𝔽2) |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^5,37|b^a=be,d^a=de,c^b=ce,f^c=f^36,f^d=f^36197 conjugacy classes — view the full character table.
| maximal subgroup of | #14557699, #14557702, #14557709, … |
| maximal normal subgroup of | #14557699, #14557702, #14557709, … |
| maximal quotient of | #14558005, #14558007, #14558013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 192);