Finite Group Databasebeta

← Prev (#72218832) Next (#72218834) →

C4×ΓL(1,𝔽8)⋊GL(2,𝔽3) #72218833

order4032
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×ΓL(1,𝔽8)⋊GL(2,𝔽3)

Splittings

FittingC4×C7×Q8 ⋊ C3×D3
derivedC7×SL(2,𝔽3) ⋊ C2×C3×C4
SylowC7 ⋊ C3×C4×GL(2,𝔽3)

Subgroups

subgroupG/H
center, hypercenterC2×C4A4⋊AGL(1,𝔽7)
commutator, hypocenterC7×SL(2,𝔽3)C2×C3×C4
FrattiniC22C2×A4⋊AGL(1,𝔽7)
FittingC4×C7×Q8C3×D3
socleC22×C7C2×C3×S4
prime radicalC2×ΓL(1,𝔽8)⋊GL(2,𝔽3)C2
cosocleC2×C7×SL(2,𝔽3)C22×C3
LCSG ▷ C7×SL(2,𝔽3)
UCSC1 ◁ C2×C4

374 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 52 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

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×ΓL(1,𝔽8)⋊GL(2,𝔽3)
maximal quotient ofAGL(1,𝔽5)×ΓL(1,𝔽8)⋊GL(2,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.