Finite Group Databasebeta

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C3×C7×#13133353 #49087899

order35700
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C7×#13133353

Splittings

Fitting, socle, HallC3×C52×C7×C17 ⋊ C4
derived, HallC52×C17 ⋊ C3×C4×C7
HallC52×C7×C17 ⋊ C3×C4
HallC3×C52×C17 ⋊ C4×C7
HallC3×C52×C7 ⋊ #595
HallC3×C7×C17 ⋊ #1039
HallC52×C7 ⋊ C3×#595
HallC7×C17 ⋊ C3×#1039
HallC3×C52 ⋊ C7×#595
HallC3×C17 ⋊ C7×#1039
SylowC52 ⋊ C3×C7×#595
SylowC17 ⋊ C3×C7×#1039

Subgroups

subgroupG/H
center, hypercenterC3×C7#13133353
commutator, hypocenterC52×C17C3×C4×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C17C4
prime radicalC3×C52×C7×D17C2
cosocleC52×D17C2×C3×C7
LCSG ▷ C52×C17
UCSC1 ◁ C3×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8925

Conjugacy classes & character table

2688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 373);