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C4×C5×C22⋊SL(2,𝔽3) #14511381

order1920
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC4×C5×C22⋊SL(2,𝔽3)

Splittings

Fitting, HallC22×C4×C5×Q8 ⋊ C3
derivedC22×Q8 ⋊ C3×C4×C5
SylowC22×C4×Q8 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5C22⋊A4
commutator, hypocenterC22×Q8C3×C4×C5
FrattiniC22C2×C5×C22⋊A4
FittingC22×C4×C5×Q8C3
socleC24×C5C2×A4
prime radicalC2×C5×C22⋊SL(2,𝔽3)C2
cosocleC23×Q8C2×C3×C5
LCSG ▷ C22×Q8
UCSC1 ◁ C2×C4×C5

658 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 658 conjugacy classes of subgroups — too many to draw. Only its 68 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

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237079);