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C2×AGL(1,𝔽5)×#272 #72217971

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

Aliases

direct productC2×AGL(1,𝔽5)×#272

Splittings

FittingC2×C5×H(3,𝔽3) ⋊ C2×C4
derived, HallC5×H(3,𝔽3) ⋊ C22×C4
SylowH(3,𝔽3) ⋊ C22×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×#272

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊D3×AGL(1,𝔽5)
commutator, hypocenterC5×H(3,𝔽3)C22×C4
FrattiniC3C2×C3⋊D3×AGL(1,𝔽5)
FittingC2×C5×H(3,𝔽3)C2×C4
socleC2×C3×C5C4×C3⋊D3
prime radicalC2×D5×#272C2
cosocleD5×H(3,𝔽3)C23
LCSG ▷ C5×H(3,𝔽3)
UCSC1 ◁ C2×C3

594 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 92 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)×((C3⋊D3)⋊C3)⋊C2, C2×C3×AGL(1,𝔽5)×#272, D3×AGL(1,𝔽5)×#272
maximal normal subgroup ofC2×AGL(1,𝔽5)×((C3⋊D3)⋊C3)⋊C2, C2×C3×AGL(1,𝔽5)×#272
maximal quotient ofC2×C3×AGL(1,𝔽5)×#272, D3×AGL(1,𝔽5)×#272

GAP

Past the SmallGroups library coverage — no SmallGroups id.