Finite Group Databasebeta

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#106×PSU(3,𝔽2) #72245000

order2304
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct product#106×PSU(3,𝔽2)

Splittings

FittingC32×#106 ⋊ Q8
SylowC32 ⋊ Q8×#106

Subgroups

subgroupG/H
centerC22D4×PSU(3,𝔽2)
commutatorC4×C3⋊D3C23×C4
FrattiniC2×C4C22×PSU(3,𝔽2)
FittingC32×#106Q8
socleC22×C32D4×Q8
prime radicalC22×C3⋊D3C22×D4
cosocleC2×C4×C3⋊D3C24
hypercenter#106PSU(3,𝔽2)
hypocenterC32Q8×#106
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

903 conjugacy classes of subgroups; only the 269 normal subgroups are shown.

normal subgroups only

This group has 903 conjugacy classes of subgroups — too many to draw. Only its 269 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) = 288

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#106×PSU(3,𝔽2)⋊C3
maximal normal subgroup of#106×PSU(3,𝔽2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.