Finite Group Databasebeta

← Prev (#72217586) Next (#72217588) →

C2×AGL(1,𝔽5)×(C3⋊D3)⋊C3 #72217587

order2160
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×AGL(1,𝔽5)×(C3⋊D3)⋊C3

Splittings

FittingC2×C5×H(3,𝔽3) ⋊ C2×C4
derivedC32×C5 ⋊ C22×C3×C4
HallC5×H(3,𝔽3) ⋊ C22×C4
SylowH(3,𝔽3) ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×(C3⋊D3)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×(C3⋊D3)⋊C3
commutator, hypocenterC32×C5C22×C3×C4
FrattiniC3C2×C3×D3×AGL(1,𝔽5)
FittingC2×C5×H(3,𝔽3)C2×C4
socleC2×C3×C5C3×C4×D3
prime radicalC2×D5×(C3⋊D3)⋊C3C2
cosocleC32×D5C23×C3
LCSG ▷ C32×C5
UCSC1 ◁ C2

410 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 94 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

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×PSU(3,𝔽2)⋊C3, C2×C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3, C2×AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊C2
maximal normal subgroup ofC2×C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3, C2×AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊C2
maximal quotient ofC2×C3×AGL(1,𝔽5)×(C3⋊D3)⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.