Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D223 |
| Fitting | C2×Q8×C223 ⋊ C2 |
| Sylow | C223 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D223 |
| commutator | C2×C223 | C24 |
| Frattini | C2 | C23×D223 |
| Fitting | C2×Q8×C223 | C2 |
| socle | C22×C223 | C23 |
| hypercenter | C2×Q8 | D223 |
| hypocenter | C223 | C22×Q8 |
| LCS | G ▷ C2×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
156 conjugacy classes of subgroups.
1130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D223, #103×D223, #28383587, … |
| maximal normal subgroup of | #101×D223, #103×D223, #28383587, … |
| maximal quotient of | C2×C4⋊C4×D223, C4×Q8×D223, C2×#20297269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 185);