Finite Group Databasebeta

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C5×#6500⋊C3 #72218355

order3360
automorphism?
homologyAbelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#6500⋊C3

Splittings

FittingC2×C5×C7×D4 ⋊ C2×C3
HallC5×#6500 ⋊ C3
Hall#6500 ⋊ C3×C5
HallC5×ΓL(1,𝔽8) ⋊ #120
HallC5×C7 ⋊ C3×#120
HallΓL(1,𝔽8) ⋊ C5×#120
SylowC7 ⋊ C3×C5×#120

Subgroups

subgroupG/H
centerC22×C5C22×AGL(1,𝔽7)
commutator, cosocleC22×C7C23×C3×C5
FrattiniC22C22×C5×AGL(1,𝔽7)
FittingC2×C5×C7×D4C2×C3
socleC22×C5×C7C23×C3
hypercenterC2×C5×D4AGL(1,𝔽7)
hypocenterC7C3×C5×#120
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

520 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 126 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

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

Relationships

maximal subgroup ofD5×#6500⋊C3, C5×#120×AGL(1,𝔽7), #72218535
maximal normal subgroup ofD5×#6500⋊C3, C5×#120×AGL(1,𝔽7), #72218535

GAP

Past the SmallGroups library coverage — no SmallGroups id.