Finite Group DatabasebetaFinite Group Databasebeta| order | 26852 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C137 ⋊ C4 |
| Sylow | C137 ⋊ #5997 |
| Sylow | C72 ⋊ #10587739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C137 | C4 |
| prime radical, cosocle | C7⋊D959 | C2 |
| LCS | G ▷ C72×C137 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1918 |
Polycyclic presentation:
2^2,7^2,137|a^2=b,c^a=c^4d^3,d^a=c^6d^3,e^a=e^100,c^b=c^6,d^b=d^6,e^b=e^1361682 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26852, 20);