Finite Group DatabasebetaFinite Group Databasebeta| order | 18473 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C13 · Schur multiplier (H2) = C7 |
| Fitting, socle | C7×C13×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C72×C13 |
| Hall | C13×C29 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C72×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C7×C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2639 |
1001 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C13×D29⋊C7, C7×C13⋊(D29⋊C7), C7×D13×C29⋊C7, … |
| maximal normal subgroup of | C7×C13×D29⋊C7, C7×C13⋊(D29⋊C7), C7×D13×C29⋊C7, … |
| maximal quotient of | C2×C7×C13×C29⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18473, 4);