Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C13×#3862 ⋊ C3×C4 |
| Hall | C13×ΓL(1,𝔽8)2 ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | ΓL(1,𝔽8)2 ⋊ Dic13 |
| Sylow | C72 ⋊ C3×Dic39 |
| Sylow | C13 ⋊ #10596868⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #26039565 |
| commutator, hypocenter | C13×#3862 | C3×C4 |
| Fitting, socle | C2×C72×C13 | C3×D3 |
| prime radical | C2×C13×ΓL(1,𝔽8)2 | C2 |
| cosocle | C2×C13×#3862 | C2×C3 |
| LCS | G ▷ C13×#3862 | |
| UCS | C1 ◁ C2 | |
104 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 364 |
Polycyclic presentation:
2,3^2,13,7^2,2|a^2=g,c^a=c^2,d^a=d^12,e^a=e^2f^3,f^a=e^6f^5,e^b=e^4,f^b=f^4,e^c=e^4f^4,f^c=f^2340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 628);