Finite Group DatabasebetaFinite Group Databasebeta| order | 18896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#17990007 |
| unambiguous semidirect product | (C2×#17990007)⋊C2 |
| Fitting | C22×C1181 ⋊ C4 |
| Sylow | C1181 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4724 |
Polycyclic presentation:
2^4,1181|a^2=d,b^a=bc,e^a=e^938,e^d=e^11801190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49180461, #49180462, C2×C22⋊#17990007, … |
| maximal normal subgroup of | #49180461, #49180462, C2×C22⋊#17990007, … |
| maximal quotient of | (C2×#17990007)⋊C4, C22⋊#22628136, #49180460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18896, 45);