Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C191 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D191 |
| commutator | C2×C191 | C22×C4 |
| Frattini | C22 | C22×D191 |
| Fitting | C22×C4×C191 | C2 |
| socle | C22×C191 | C23 |
| hypercenter | C22×C4 | D191 |
| hypocenter | C191 | #117 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,191|a^2=e,c^2=d,b^a=bd,f^a=f^1901540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27132419, #27132420, #27132423, … |
| maximal normal subgroup of | #27132419, #27132420, #27132423, … |
| maximal quotient of | #27132509, C4×C22⋊Dic191, C4×C4⋊Dic191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 105);