Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C191⋊#95 |
| Sylow | C191 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D191 |
| commutator | C2×C191 | C42 |
| Fitting | C22×C4×C191 | C2 |
| socle | C23×C191 | C22 |
| hypercenter | C22×C4 | D191 |
| hypocenter | C191 | #95 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,191|a^2=d,b^2=e,b^a=bc,f^b=f^1901540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27132397, #27132398, #27132400, … |
| maximal normal subgroup of | #27132397, #27132398, #27132400, … |
| maximal quotient of | #27132417, #27132418, #27132419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 53);