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C9×C31×#1035 #42124288

order27900
isoclinismisoclinic class of #1035
automorphism?
homologyAbelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC9×C31×#1035

Splittings

Fitting, HallC9×C25×C31 ⋊ C4
derived, SylowC25 ⋊ C4×C9×C31
HallC25×C31 ⋊ C4×C9
HallC9×C25 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC9×C31#1035
commutator, hypocenterC25C4×C9×C31
FrattiniC3×C5C3×AGL(1,𝔽5)×C31
FittingC9×C25×C31C4
socleC3×C5×C31C3×AGL(1,𝔽5)
prime radicalC3×C31×D25C2×C3
cosocleC3×D25C2×C3×C31
LCSG ▷ C25
UCSC1 ◁ C9×C31

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 35);