Finite Group Databasebeta

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C3×#10598722 #14277159

order1920
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C22

Aliases

direct productC3×#10598722

Splittings

HallC3×C5 ⋊ #1295
SylowC5 ⋊ C3×#1295

Subgroups

subgroupG/H
centerC23×C3C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C3×C42
FrattiniC22×C4C2×C3×AGL(1,𝔽5)
FittingC2×C3×C5×C4⋊C4C4
socle, prime radicalC23×C3×C5C22⋊C4
cosocleC2×C4×Dic5C22×C3
hypercenterC2×C3×C4⋊C4AGL(1,𝔽5)
hypocenterC5C3×#1295
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×C4⋊C4

360 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 1920

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 2857);