Finite Group Databasebeta

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C5×D7×#120 #72218506

order2240
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C27

Aliases

direct productC5×D7×#120

Splittings

FittingC5×C7×#120 ⋊ C2
HallC5×C7 ⋊ C2×#120
SylowC7 ⋊ C2×C5×#120

Subgroups

subgroupG/H
centerC22×C5C23×D7
commutator, cosocleC22×C7C24×C5
FrattiniC22C23×C5×D7
FittingC5×C7×#120C2
socleC22×C5×C7C24
hypercenterC5×#120D7
hypocenterC7C2×C5×#120
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C5 ◁ C5×#120

1324 conjugacy classes of subgroups; only the 262 normal subgroups are shown.

normal subgroups only

This group has 1324 conjugacy classes of subgroups — too many to draw. Only its 262 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

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

Relationships

maximal subgroup ofC5×#120×AGL(1,𝔽7), D5×D7×#120
maximal normal subgroup ofC5×#120×AGL(1,𝔽7), D5×D7×#120

GAP

Past the SmallGroups library coverage — no SmallGroups id.