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C5×#4294⋊Dic7 #37560897

order23940
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×#4294⋊Dic7
unambiguous semidirect product#4294⋊(C5×Dic7)

Splittings

derived, HallC7×C19 ⋊ C4×C5×C9
HallC5×C7×#4294 ⋊ C4
HallC5×Dic133 ⋊ C9
HallC7×#4294 ⋊ C4×C5
HallC5×#4294 ⋊ Dic7
HallC5×C7×C19 ⋊ C4×C9
HallDic133 ⋊ C5×C9
Hall#4294 ⋊ C5×Dic7
HallC5×C19 ⋊ C9×Dic7
HallC5×C7 ⋊ #4294⋊C4
SylowC19 ⋊ C5×C9×Dic7
SylowC7 ⋊ C5×#4294⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5(C19⋊C3)⋊D7
commutator, hypocenterC7×C19C4×C5×C9
FrattiniC2×C3C5×(C19⋊C3)⋊D7
Fitting, socle, prime radicalC2×C3×C5×C7×C19C2×C3
cosocleC2×C3×C7×C19C2×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23940

Conjugacy classes & character table

1080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 29);