Finite Group DatabasebetaFinite Group Databasebeta| order | 24108 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, Hall | C72×C41 ⋊ Dic3 |
| derived, Hall | C41×#3862 ⋊ C4 |
| Hall | #3862 ⋊ #4223 |
| Sylow | C72 ⋊ C3⋊#4223 |
| Sylow | C41 ⋊ #10596885 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C41×#3862 | C4 |
| Fitting, socle | C72×C41 | Dic3 |
| prime radical, cosocle | C41⋊#64425 | C2 |
| LCS | G ▷ C41×#3862 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 574 |
Polycyclic presentation:
2^2,3,41,7^2|a^2=b,c^a=c^2,d^a=d^32,e^a=e^3f^4,f^a=ef^4,d^b=d^40,e^b=e^6,f^b=f^6,e^c=e^2f^6,f^c=f^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24108, 82);