Finite Group Databasebeta

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C2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3 #72217649

order25920
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32

Aliases

direct productC2×C3×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3

Splittings

Fitting, socleC2×C33×C5 ⋊ C4×SL(2,𝔽3)
derivedC5×PSU(3,𝔽2) ⋊ C2×C32×C4
SylowC5 ⋊ C2×C3×C4×PSU(3,𝔽2)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3
commutator, hypocenterC5×PSU(3,𝔽2)C2×C32×C4
FrattiniC1G
Fitting, socleC2×C33×C5C4×SL(2,𝔽3)
prime radicalC2×C3×D5×PSU(3,𝔽2)⋊C3C2
cosocleD5×PSU(3,𝔽2)C22×C32
LCSG ▷ C5×PSU(3,𝔽2)
UCSC1 ◁ C2×C3

1724 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(2,𝔽3)
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×AGL(2,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.