Finite Group Databasebeta

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C7×#13133334⋊C3 #49087672

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

Aliases

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

Splittings

derived, HallC52×C17 ⋊ C3×C4×C7
HallC7×#13133334 ⋊ C3
HallC7×C17×C52⋊C3 ⋊ C4
HallC52×C7×C17 ⋊ C3×C4
Hall#13133334 ⋊ C3×C7
HallC17×C52⋊C3 ⋊ C4×C7
HallC7×C52⋊C3 ⋊ Dic17
HallC52×C7 ⋊ C3×Dic17
HallC7×C17 ⋊ #1039⋊C3
HallC52⋊C3 ⋊ C7×Dic17
SylowC52 ⋊ C3×C7×Dic17
SylowC17 ⋊ C7×#1039⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7C17⋊((C5⋊D5)⋊C3)
commutator, hypocenterC52×C17C3×C4×C7
FrattiniC2C7×C17⋊((C5⋊D5)⋊C3)
Fitting, socleC2×C52×C7×C17C2×C3
prime radicalC2×C7×C17×C52⋊C3C2
cosocleC2×C52×C17C2×C3×C7
LCSG ▷ C52×C17
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7140

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 146);