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C5×(C7⋊C9)⋊Dic19 #37560898

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

Aliases

direct productC5×(C7⋊C9)⋊Dic19
unambiguous semidirect product(C7⋊C9)⋊(C5×Dic19)

Splittings

derived, HallC7×C19 ⋊ C4×C5×C9
HallC5×C19×C7⋊C9 ⋊ C4
HallC5×Dic133 ⋊ C9
HallC19×C7⋊C9 ⋊ C4×C5
HallC5×C7×C19 ⋊ C4×C9
HallDic133 ⋊ C5×C9
HallC5×C7⋊C9 ⋊ Dic19
HallC5×C19 ⋊ Dic7⋊C9
HallC7⋊C9 ⋊ C5×Dic19
HallC5×C7 ⋊ C9×Dic19
SylowC19 ⋊ C5×Dic7⋊C9
SylowC7 ⋊ C5×C9×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5ΓL(1,𝔽8)⋊D19
commutator, hypocenterC7×C19C4×C5×C9
FrattiniC2×C3C5×ΓL(1,𝔽8)⋊D19
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

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 30);