Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C191 ⋊ C2 |
| Sylow | C191 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D191 |
| commutator, socle | C2×C191 | C2×C8 |
| Fitting | C16×C191 | C2 |
| hypercenter | C16 | D191 |
| hypocenter | C191 | M32 |
| LCS | G ▷ C2×C191 ▷ C191 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,191|a^2=c,c^2=d,d^2=e,b^a=be,f^b=f^1901540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M32×D191, C2×#20259261, #27133079, … |
| maximal normal subgroup of | M32×D191, C2×#20259261, #27133079, … |
| maximal quotient of | #27132438, (C2×D191)⋊C16, Dic191⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 85);