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AGL(1,𝔽5)×3−1+4 #72247190

order4860
automorphism?
homologyAbelianization (H1) = C34×C4 · Schur multiplier (H2) = C35

Aliases

direct productAGL(1,𝔽5)×3−1+4

Splittings

Fitting, HallC5×3−1+4 ⋊ C4
SylowC5 ⋊ C4×3−1+4

Subgroups

subgroupG/H
center, FrattiniC3C34×AGL(1,𝔽5)
commutator, socleC3×C5C34×C4
FittingC5×3−1+4C4
prime radicalC3×D5×H(3,𝔽3)C2×C3
cosocleC3×D5C2×C34
hypercenter3−1+4AGL(1,𝔽5)
hypocenterC5C4×3−1+4
LCSG ▷ C3×C5 ▷ C5
UCSC1 ◁ C3 ◁ 3−1+4

1380 conjugacy classes of subgroups; only the 852 normal subgroups are shown.

normal subgroups only

This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 852 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽5)×#10624749, AGL(1,𝔽5)×#4207⋊C3, AGL(1,𝔽5)×#92394
maximal normal subgroup ofAGL(1,𝔽5)×#10624749, AGL(1,𝔽5)×#4207⋊C3, AGL(1,𝔽5)×#92394

GAP

Past the SmallGroups library coverage — no SmallGroups id.