Finite Group Databasebeta

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#100×PSU(3,𝔽2) #72220473

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

Aliases

direct product#100×PSU(3,𝔽2)

Splittings

FittingC32×#100 ⋊ Q8
SylowC32 ⋊ Q8×#100

Subgroups

subgroupG/H
centerC2C22⋊C4×PSU(3,𝔽2)
commutatorC22×C3⋊D3C23×C4
FrattiniC2×C4C22×PSU(3,𝔽2)
FittingC32×#100Q8
socleC2×C32Q8×C22⋊C4
prime radicalC2×D4×C3⋊D3C23
cosocleC2×C4×C3⋊D3C24
hypercenter#100PSU(3,𝔽2)
hypocenterC32Q8×#100
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

1291 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 1291 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#100×PSU(3,𝔽2)⋊C3, #453×PSU(3,𝔽2)
maximal normal subgroup of#100×PSU(3,𝔽2)⋊C3, #453×PSU(3,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.