Finite Group Databasebeta

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C4×C5×#95⋊C3 #14510666

order1920
isoclinismisoclinic class of #95⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC4×C5×#95⋊C3
unambiguous semidirect product(C4×#95)⋊(C3×C5)
unambiguous semidirect product(C4×C5×#95)⋊C3

Splittings

Fitting, HallC4×C5×#95 ⋊ C3
derived#95 ⋊ C3×C4×C5
SylowC4×#95 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5C42⋊C3
commutator, hypocenter#95C3×C4×C5
FrattiniC24C2×C5×A4
FittingC4×C5×#95C3
socleC24×C5C2×A4
prime radicalC2×C5×#95⋊C3C2
cosocleC2×#95C2×C3×C5
LCSG ▷ #95
UCSC1 ◁ C2×C4×C5

314 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 240

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236364);