Finite Group Databasebeta

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C9⋊C9×#997 #72276129

order7776
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C23×C33

Aliases

direct productC9⋊C9×#997

Splittings

FittingH(5,𝔽2)×C9⋊C9 ⋊ C3
SylowH(5,𝔽2) ⋊ C3×C9⋊C9

Subgroups

subgroupG/H
center, Frattini, socleC2×C32C32×C22⋊A4
commutatorC3×H(5,𝔽2)C32×C9
FittingH(5,𝔽2)×C9⋊C9C3
prime radicalC32×#997C32
cosocleC32×H(5,𝔽2)C33
hypercenterC2×C9⋊C9C22⋊A4
hypocenterH(5,𝔽2)C3×C9⋊C9
LCSG ▷ C3×H(5,𝔽2) ▷ H(5,𝔽2)
UCSC1 ◁ C2×C32 ◁ C2×C9⋊C9

1398 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 1398 conjugacy classes of subgroups — too many to draw. Only its 170 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) = 648

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72276206
maximal normal subgroup of#72276206

GAP

Past the SmallGroups library coverage — no SmallGroups id.