Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C191 · Schur multiplier (H2) = C25 |
| direct product | 2−1+4×C191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C191 | C24 |
| commutator, Frattini, cosocle | C2 | C24×C191 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C191 ◁ G | |
146 conjugacy classes of subgroups.
3247 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #454×C191, #456×C191, #577×C191, … |
| maximal normal subgroup of | #454×C191, #456×C191, #577×C191, … |
| maximal quotient of | #519×C191, #520×C191, #536×C191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 50);