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H(5,𝔽2)×PSU(3,𝔽2) #72220437

order2304
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213×C3

Aliases

direct productH(5,𝔽2)×PSU(3,𝔽2)

Splittings

FittingC32×H(5,𝔽2) ⋊ Q8
SylowC32 ⋊ Q8×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2C24×PSU(3,𝔽2)
commutator, cosocleC2×C3⋊D3C26
FittingC32×H(5,𝔽2)Q8
socleC2×C32C24×Q8
prime radicalC3⋊D3×H(5,𝔽2)C22
hypercenterH(5,𝔽2)PSU(3,𝔽2)
hypocenterC32Q8×H(5,𝔽2)
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2 ◁ H(5,𝔽2)

7855 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofH(5,𝔽2)×PSU(3,𝔽2)⋊C3, H(5,𝔽2)×AΓL(1,𝔽9), B(4,𝔽2)×PSU(3,𝔽2), …
maximal normal subgroup ofH(5,𝔽2)×PSU(3,𝔽2)⋊C3, H(5,𝔽2)×AΓL(1,𝔽9), B(4,𝔽2)×PSU(3,𝔽2), …

GAP

Past the SmallGroups library coverage — no SmallGroups id.