Finite Group Databasebeta

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C7×C5⋊(#66526⋊C2) #37552043

order23310
automorphism?
homologyAbelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C5⋊(#66526⋊C2)
unambiguous semidirect productC5⋊(C7×#66526⋊C2)
unambiguous semidirect product#66526⋊(C7×D5)

Splittings

Fitting, socle, HallC5×C7×C37 ⋊ C2×C9
derived, HallC5×C37 ⋊ C2×C7×C9
HallC5×C7×#66526 ⋊ C2
HallC7×D185 ⋊ C9
HallC7×#66526 ⋊ D5
HallC5×#66526 ⋊ C2×C7
HallD185 ⋊ C7×C9
Hall#66526 ⋊ C7×D5
HallC7×C37 ⋊ C9×D5
SylowC37 ⋊ C7×C9×D5
HallC5×C7 ⋊ #66526⋊C2
SylowC5 ⋊ C7×#66526⋊C2

Subgroups

subgroupG/H
center, hypercenterC7C5⋊(#66526⋊C2)
commutator, hypocenterC5×C37C2×C7×C9
FrattiniC1G
Fitting, socleC5×C7×C37C2×C9
prime radicalC7×C5⋊(D37⋊C3)C3
cosocleC5×C37⋊C3C2×C3×C7
LCSG ▷ C5×C37
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1295

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 62);