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#11925241

order1200
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C5

Aliases

No aliases for this group.

Splittings

FittingC3×C52×C8 ⋊ C2
HallC3×C52 ⋊ SD16
SylowC52 ⋊ #204
SylowC3 ⋊ #87800

Subgroups

subgroupG/H
centerC2C4⋊(C3⋊(C5⋊D5))
commutator, cosocleC3×C4×C52C22
FrattiniC4C2×C3⋊(C5⋊D5)
FittingC3×C52×C8C2
socleC2×C3×C52D4
prime radicalC4⋊(C3⋊(C5⋊D5))C2
hypercenterC8C3⋊(C5⋊D5)
hypocenterC3×C52SD16
LCSG ▷ C3×C4×C52 ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C2 ◁ C4 ◁ C8

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 600

Polycyclic presentation:

2^4,3,5^2|b^2=c,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^4,g^a=g^4

Conjugacy classes & character table

303 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 451);