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C5×D32⋊C8 #13085554

order1440
isoclinismisoclinic class of GO+(4,𝔽2)
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22

Aliases

direct productC5×D32⋊C8
unambiguous semidirect productD32⋊(C5×C8)

Splittings

HallC32×C5 ⋊ C22⋊C8
SylowC32 ⋊ C5×C22⋊C8

Subgroups

subgroupG/H
center, hypercenterC4×C5GO+(4,𝔽2)
commutatorC3⋊D3C2×C5×C8
FrattiniC4C5×GO+(4,𝔽2)
FittingC32×C4×C5D4
socleC2×C32×C5C22⋊C4
prime radicalC2×C5×D32C4
cosocleC4×C3⋊D3C22×C5
hypocenterC32C5×C22⋊C8
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C4×C5

176 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 19 points:

(1,2,3,4,5)(6,8)(7,10,11)(12,13,14,16,15,17,18,19);(6,7)(8,11)(9,10)

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1871);