Finite Group DatabasebetaFinite Group Databasebeta| order | 18884 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C4721 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4721 | C4 |
| prime radical, cosocle | D4721 | C2 |
| LCS | G ▷ C4721 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4721 |
Polycyclic presentation:
2^2,4721|a^2=b,c^a=c^1697,c^b=c^47201184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34038510, #49180078 |
| maximal normal subgroup of | C2×#34038510, #49180078 |
| maximal quotient of | #49180076, C2×#34038510 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18884, 3);