Finite Group Databasebeta

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AGL(1,𝔽5)×#92394 #72247511

order9720
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productAGL(1,𝔽5)×#92394

Splittings

Fitting, HallC5×3−1+4 ⋊ C2×C4
Sylow3−1+4 ⋊ C2×AGL(1,𝔽5)
SylowC5 ⋊ C4×#92394

Subgroups

subgroupG/H
center, FrattiniC3C32×C3⋊D3×AGL(1,𝔽5)
commutator, hypocenterC5×H(3,𝔽3)C2×C32×C4
FittingC5×3−1+4C2×C4
socleC3×C5C32×C4×C3⋊D3
prime radicalC3×D5×#272C2×C3
cosocleD5×H(3,𝔽3)C22×C32
hypercenter3−1+2C3⋊D3×AGL(1,𝔽5)
LCSG ▷ C5×H(3,𝔽3)
UCSC1 ◁ C3 ◁ 3−1+2

1288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽5)×(#4207⋊C2)⋊C3
maximal normal subgroup ofAGL(1,𝔽5)×(#4207⋊C2)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.