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C37⋊C3×3−1+4 #41008254

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

Aliases

direct productC37⋊C3×3−1+4

Splittings

FittingC37×3−1+4 ⋊ C3
SylowC37 ⋊ C3×3−1+4

Subgroups

subgroupG/H
center, FrattiniC3C34×C37⋊C3
commutator, socle, cosocleC3×C37C35
FittingC37×3−1+4C3
prime radicalC3×H(3,𝔽3)×C37⋊C3C3
hypercenter3−1+4C37⋊C3
hypocenterC37C3×3−1+4
LCSG ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ 3−1+4

5588 conjugacy classes of subgroups; only the 2881 normal subgroups are shown.

normal subgroups only

This group has 5588 conjugacy classes of subgroups — too many to draw. Only its 2881 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) = 999

Conjugacy classes & character table

1245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 4025);