Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#22602390 |
| Fitting | C2×D4×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#3520 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D71 |
| commutator, cosocle | C22×C71 | C26 |
| Frattini | C22 | C25×D71 |
| Fitting | C2×D4×Q8×C71 | C2 |
| socle | C23×C71 | C25 |
| hypercenter | C2×D4×Q8 | D71 |
| hypocenter | C71 | C2×#3520 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C2×D4×Q8 | |
7910 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
1838 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 1077568);