Finite Group Databasebeta

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C2×AGL(1,𝔽5)×D28 #72217857

order2240
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×AGL(1,𝔽5)×D28

Splittings

FittingC2×C4×C5×C7 ⋊ C2×C4
HallC5×C7 ⋊ C2×C4×D4
SylowC7 ⋊ C2×D4×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×D28

Subgroups

subgroupG/H
centerC22C2×D7×AGL(1,𝔽5)
commutatorC2×C5×C7C23×C4
FrattiniC2C22×D7×AGL(1,𝔽5)
FittingC2×C4×C5×C7C2×C4
socleC22×C5×C7C22×C4
prime radicalC2×D5×D28C2
cosocleC2×C7×D5C24
hypercenterC2×C4D7×AGL(1,𝔽5)
hypocenterC5×C7C2×C4×D4
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C22 ◁ C2×C4

852 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 210 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

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×C4⋊AGL(1,𝔽7), C2×D4×D7×AGL(1,𝔽5), AGL(1,𝔽5)×#6471, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×C4⋊AGL(1,𝔽7), C2×D4×D7×AGL(1,𝔽5), AGL(1,𝔽5)×#6471, …
maximal quotient ofAGL(1,𝔽5)×#6471, AGL(1,𝔽5)×#6445

GAP

Past the SmallGroups library coverage — no SmallGroups id.