Finite Group Databasebeta

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C3×#22582679 #41008257

order26973
automorphism?
homologyAbelianization (H1) = C35 · Schur multiplier (H2) = C39

Aliases

direct productC3×#22582679

Splittings

FittingC32×3−1+2×C37 ⋊ C3
SylowC37 ⋊ C3×3−1+4

Subgroups

subgroupG/H
centerC32C33×C37⋊C3
commutator, cosocleC3×C37C35
FrattiniC3C34×C37⋊C3
FittingC32×3−1+2×C37C3
socleC32×C37C34
prime radicalC32×C32⋊(C37⋊C3)C3
hypercenterC32×3−1+2C37⋊C3
hypocenterC37C3×3−1+4
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C32 ◁ C32×3−1+2

5588 conjugacy classes of subgroups; only the 2884 normal subgroups are shown.

normal subgroups only

This group has 5588 conjugacy classes of subgroups — too many to draw. Only its 2884 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2997

Conjugacy classes & character table

1437 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4028);