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C2×C5×C8×AGL(1,𝔽5) #13104476

order1600
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C5×C8×AGL(1,𝔽5)

Splittings

FittingC2×C52×C8 ⋊ C4
derivedC5 ⋊ C2×C4×C5×C8
SylowC52 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C5×C8AGL(1,𝔽5)
commutator, hypocenterC5C2×C4×C5×C8
FrattiniC4C22×C5×AGL(1,𝔽5)
FittingC2×C52×C8C4
socleC22×C52C42
prime radicalC22×C5×D5C2×C4
cosocleC4×D5C23×C5
LCSG ▷ C5
UCSC1 ◁ C2×C5×C8

335 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6828);