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C5×#64883 #13100072

order1600
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2

Aliases

direct productC5×#64883

Splittings

SylowC52 ⋊ #334

Subgroups

subgroupG/H
centerC22×C5C4⋊AGL(1,𝔽5)
commutatorC4×C5C2×C5×C8
FrattiniC2×C4C2×C5×AGL(1,𝔽5)
FittingC2×C52×C8C4
socle, prime radicalC22×C52C4⋊C4
cosocleC4×Dic5C22×C5
hypercenterC2×C5×C8AGL(1,𝔽5)
hypocenterC5C5×#334
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8

119 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2424);