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C7×C3⋊#13133334 #49087690

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

Aliases

direct productC7×C3⋊#13133334
unambiguous semidirect productC3⋊(C7×#13133334)

Splittings

derived, HallC3×C52×C17 ⋊ C4×C7
HallC3×C52×C7×C17 ⋊ C4
HallC52×C7×C17 ⋊ Dic3
HallC3×C52×C7 ⋊ Dic17
HallC52×C17 ⋊ C7×Dic3
HallC3×C7×C17 ⋊ #1039
HallC52×C7 ⋊ Dic51
HallC7×C17 ⋊ C3⋊#1039
HallC3×C52 ⋊ C7×Dic17
HallC3×C17 ⋊ C7×#1039
SylowC52 ⋊ C7×Dic51
HallC3×C7 ⋊ #13133334
SylowC17 ⋊ C7×C3⋊#1039
SylowC3 ⋊ C7×#13133334

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊D85)
commutator, hypocenterC3×C52×C17C4×C7
FrattiniC2C7×C3⋊(C5⋊D85)
Fitting, socle, prime radicalC2×C3×C52×C7×C17C2
cosocleC2×C3×C52×C17C2×C7
LCSG ▷ C3×C52×C17
UCSC1 ◁ C2×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35700

Conjugacy classes & character table

8946 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 164);