Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C101 · Schur multiplier (H2) = C29 |
| direct product | C2×#520×C101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C101 | C24 |
| commutator | C2 | C24×C4×C101 |
| Frattini, cosocle | C22 | C25×C101 |
| prime radical | C22×#41×C101 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C101 ◁ G | |
1640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6464 |
6868 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C101×#8324, C101×#10765, C101×#10775, … |
| maximal normal subgroup of | C101×#8324, C101×#10765, C101×#10775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 2159);