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C5×C22⋊C4×SL(2,𝔽3) #14510898

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×C22⋊C4×SL(2,𝔽3)
unambiguous semidirect product(Q8×C22⋊C4)⋊(C3×C5)
unambiguous semidirect product(C5×Q8×C22⋊C4)⋊C3

Splittings

Fitting, HallC5×Q8×C22⋊C4 ⋊ C3
SylowQ8×C22⋊C4 ⋊ C3×C5

Subgroups

subgroupG/H
center, socleC23×C5C22×A4
commutatorC2×Q8C2×C3×C4×C5
FrattiniC23C22×C5×A4
FittingC5×Q8×C22⋊C4C3
prime radicalC23×C5×SL(2,𝔽3)C2
cosocleC22×Q8C22×C3×C5
hypercenterC2×C5×C22⋊C4A4
hypocenterQ8C3×C5×C22⋊C4
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C23×C5 ◁ C2×C5×C22⋊C4

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

normal subgroups only

This group has 550 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) = 320

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236596);