Finite Group Databasebeta

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C3×#1035×C127 #49185337

order38100
automorphism?
homologyAbelianization (H1) = C3×C4×C127 · Schur multiplier (H2) = C1

Aliases

direct productC3×#1035×C127

Splittings

Fitting, HallC3×C25×C127 ⋊ C4
derived, SylowC25 ⋊ C3×C4×C127
HallC25×C127 ⋊ C3×C4
HallC3×C25 ⋊ C4×C127

Subgroups

subgroupG/H
center, hypercenterC3×C127#1035
commutator, hypocenterC25C3×C4×C127
FrattiniC5C3×AGL(1,𝔽5)×C127
FittingC3×C25×C127C4
socleC3×C5×C127AGL(1,𝔽5)
prime radicalC3×D25×C127C2
cosocleD25C2×C3×C127
LCSG ▷ C25
UCSC1 ◁ C3×C127

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9525

Conjugacy classes & character table

3810 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38100, 20);