Finite Group Databasebeta

C32×C32⋊#66524 #41007488

order26973
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C37

Aliases

direct productC32×C32⋊#66524

Splittings

SylowC37 ⋊ C32×C32⋊C9

Subgroups

subgroupG/H
centerC34C3×C37⋊C3
commutatorC3×C37C33×C9
FrattiniC32C33×C37⋊C3
Fitting, prime radicalC35×C37C3
socleC34×C37C32
cosocleC32×C37C34
hypercenterC35C37⋊C3
hypocenterC37C32×C32⋊C9
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C34 ◁ C35

2996 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8991

Conjugacy classes & character table

3213 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3259);