Finite Group DatabasebetaFinite Group Databasebeta| order | 8824 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C1103⋊C8 |
| derived, Sylow | C1103 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D1103 |
| commutator, hypocenter | C1103 | C8 |
| Fitting | C4×C1103 | C2 |
| socle | C2×C1103 | C4 |
| LCS | G ▷ C1103 | |
| UCS | C1 ◁ C4 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1103|a^2=b,b^2=c,d^a=d^11022212 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D1103, C2×C1103⋊C8, #31798805, … |
| maximal normal subgroup of | C8×D1103, C2×C1103⋊C8, #31798805, … |
| maximal quotient of | C1103⋊C16, C2×C1103⋊C8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8824, 6);