Finite Group Databasebeta

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3−1+2×#11758608 #41007832

order26973
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C34

Aliases

direct product3−1+2×#11758608

Splittings

SylowC37 ⋊ 3−1+22

Subgroups

subgroupG/H
center, FrattiniC32C33×C37⋊C3
commutator, socle, cosocleC32×C37C34
FittingC32×3−1+2×C37C3
prime radicalC34×C37C32
hypercenterC32×3−1+2C37⋊C3
hypocenterC373−1+22
LCSG ▷ C32×C37 ▷ C37
UCSC1 ◁ C32 ◁ C32×3−1+2

836 conjugacy classes of subgroups; only the 316 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 316 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

1309 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26973, 3603);