Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D1528 |
| Fitting | C2×C8×C191 ⋊ C2 |
| Sylow | C191 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D764 |
| commutator | C4×C191 | C23 |
| Frattini | C4 | C22×D191 |
| Fitting | C2×C8×C191 | C2 |
| socle | C22×C191 | D4 |
| hypercenter | C2×C8 | D191 |
| hypocenter | C191 | C2×D8 |
| LCS | G ▷ C4×C191 ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
1534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27132463, #27132465, #27132475, … |
| maximal normal subgroup of | #27132463, #27132465, #27132475, … |
| maximal quotient of | C2×#20259244, C2×#20259256, C4×D1528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 157);