Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#16813160 |
| Sylow | C223 ⋊ C2×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D223 |
| commutator | C4×C223 | C23 |
| Frattini | C4 | C22×D223 |
| Fitting | C2×Q8×C223 | C2 |
| socle | C22×C223 | D4 |
| hypercenter | C2×Q8 | D223 |
| hypocenter | C223 | C2×Q16 |
| LCS | G ▷ C4×C223 ▷ C2×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
60 conjugacy classes of subgroups.
1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28383672, C4×#16813160, #28383684, … |
| maximal normal subgroup of | #28383672, C4×#16813160, #28383684, … |
| maximal quotient of | C2×#20297227, C2×#20297228, C2×#20297237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 163);