Finite Group Databasebeta

← Prev (#72213995) Next (#72213997) →

D32×PSU(3,𝔽2) #72213996

order2592
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25×C3

Aliases

direct productD32×PSU(3,𝔽2)

Splittings

Fitting, socle, SylowC34 ⋊ C22×Q8

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocleC32×C3⋊D3C24
Fitting, socle, hypocenterC34C22×Q8
prime radicalD32×C3⋊D3C22
LCSG ▷ C32×C3⋊D3 ▷ C34
UCSC1

785 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 785 conjugacy classes of subgroups — too many to draw. Only its 132 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

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD32×PSU(3,𝔽2)⋊C3, D32×AΓL(1,𝔽9), C2×D32×PSU(3,𝔽2), …
maximal normal subgroup ofD32×PSU(3,𝔽2)⋊C3, D32×AΓL(1,𝔽9), C2×D32×PSU(3,𝔽2), …
maximal quotient ofC2×D32×PSU(3,𝔽2), #626×PSU(3,𝔽2), #624×PSU(3,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.