Finite Group Databasebeta

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C3×#1035×C107 #44545612

order32100
automorphism?
homologyAbelianization (H1) = C3×C4×C107 · Schur multiplier (H2) = C1

Aliases

direct productC3×#1035×C107

Splittings

Fitting, HallC3×C25×C107 ⋊ C4
derived, SylowC25 ⋊ C3×C4×C107
HallC25×C107 ⋊ C3×C4
HallC3×C25 ⋊ C4×C107

Subgroups

subgroupG/H
center, hypercenterC3×C107#1035
commutator, hypocenterC25C3×C4×C107
FrattiniC5C3×AGL(1,𝔽5)×C107
FittingC3×C25×C107C4
socleC3×C5×C107AGL(1,𝔽5)
prime radicalC3×D25×C107C2
cosocleD25C2×C3×C107
LCSG ▷ C25
UCSC1 ◁ C3×C107

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8025

Conjugacy classes & character table

3210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32100, 10);