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C2×AGL(1,𝔽5)×PSU(3,𝔽2) #72217585

order2880
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct productC2×AGL(1,𝔽5)×PSU(3,𝔽2)

Splittings

Fitting, socleC2×C32×C5 ⋊ C4×Q8
HallC32×C5 ⋊ C2×C4×Q8
SylowC32 ⋊ C2×Q8×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×PSU(3,𝔽2)

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×PSU(3,𝔽2)
commutatorC5×C3⋊D3C23×C4
FrattiniC1G
Fitting, socleC2×C32×C5C4×Q8
prime radicalC2×D5×C3⋊D3C23
cosocleD5×C3⋊D3C24
hypocenterC32×C5C2×C4×Q8
LCSG ▷ C5×C3⋊D3 ▷ C32×C5
UCSC1 ◁ C2

650 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 166 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

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3, C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2), C2×AGL(1,𝔽5)×AΓL(1,𝔽9)
maximal normal subgroup ofC2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3, C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2), C2×AGL(1,𝔽5)×AΓL(1,𝔽9)
maximal quotient ofC2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)

GAP

Past the SmallGroups library coverage — no SmallGroups id.