Finite Group Databasebeta

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AGL(1,𝔽5)×SL(2,𝔽3)×AGL(1,𝔽7) #72218656

order20160
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productAGL(1,𝔽5)×SL(2,𝔽3)×AGL(1,𝔽7)

Splittings

Fitting, derivedC5×C7×Q8 ⋊ C2×C32×C4
HallQ8×D7×AGL(1,𝔽5) ⋊ C32
HallC5×C7 ⋊ C2×C3×C4×SL(2,𝔽3)
SylowC7 ⋊ C2×C3×AGL(1,𝔽5)×SL(2,𝔽3)
SylowC5 ⋊ C4×SL(2,𝔽3)×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2A4×AGL(1,𝔽5)×AGL(1,𝔽7)
commutator, Fitting, hypocenterC5×C7×Q8C2×C32×C4
socleC2×C5×C7C2×C3×C4×A4
prime radicalD5×SL(2,𝔽3)×AGL(1,𝔽7)C2
cosocleC7×Q8×D5C22×C32
LCSG ▷ C5×C7×Q8
UCSC1 ◁ C2

1144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.