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C2×AGL(1,𝔽5)×C27 #11761709

order1080
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽5)×C27
unambiguous semidirect productD5⋊(C4×C27)

Splittings

FittingC2×C5×C27 ⋊ C4
derived, SylowC5 ⋊ C2×C4×C27
HallC5×C27 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC2×C27AGL(1,𝔽5)
commutator, hypocenterC5C2×C4×C27
FrattiniC9C2×C3×AGL(1,𝔽5)
FittingC2×C5×C27C4
socleC2×C3×C5C4×C9
prime radicalC2×C3×D5C2×C9
cosocleC9×D5C22×C3
LCSG ▷ C5
UCSC1 ◁ C2×C27

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 270

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 55);