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C3×D5×#103 #11749698

order960
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×D5×#103

Splittings

FittingC3×C5×#103 ⋊ C2
HallC3×C5 ⋊ C2×#103
SylowC5 ⋊ C2×C3×#103

Subgroups

subgroupG/H
centerC22×C3D4×D5
commutatorC4×C5C22×C3×C4
FrattiniC2×C4C22×C3×D5
FittingC3×C5×#103C2
socleC22×C3×C5C2×D4
prime radicalC22×C3×D5D4
cosocleC2×C4×C5C23×C3
hypercenterC3×#103D5
hypocenterC5C2×C3×#103
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×#103

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

normal subgroups only

This group has 324 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 →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×#103, #103×ΓL(1,𝔽16), C3×#10603984, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×#103, #103×ΓL(1,𝔽16), C3×#10603984, …
maximal quotient ofC3×D5×Q8⋊C8, C3×#10599025, C3×#10599029, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3893);