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C5×C16×AGL(1,𝔽5) #13100033

order1600
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C5×C16 · Schur multiplier (H2) = C4

Aliases

direct productC5×C16×AGL(1,𝔽5)

Splittings

FittingC52×C16 ⋊ C4
derivedC5 ⋊ C4×C5×C16
SylowC52 ⋊ C4×C16

Subgroups

subgroupG/H
center, hypercenterC5×C16AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C16
FrattiniC8C2×C5×AGL(1,𝔽5)
FittingC52×C16C4
socleC2×C52C4×C8
prime radicalC2×C5×D5C2×C8
cosocleC8×D5C22×C5
LCSG ▷ C5
UCSC1 ◁ C5×C16

121 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, 2385);