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C7×C47×Dic15 #34089461

order19740
automorphism?
homologyAbelianization (H1) = C4×C7×C47 · Schur multiplier (H2) = C1

Aliases

direct productC7×C47×Dic15
unambiguous semidirect productC3⋊(C7×Dic5×C47)

Splittings

derived, HallC3×C5 ⋊ C4×C7×C47
HallC3×C5×C7×C47 ⋊ C4
HallC5×C7×C47 ⋊ Dic3
HallC3×C7×C47 ⋊ Dic5
HallC3×C5×C47 ⋊ C4×C7
HallC5×C47 ⋊ C7×Dic3
HallC3×C47 ⋊ C7×Dic5
HallC3×C5×C7 ⋊ C4×C47
HallC5×C7 ⋊ Dic3×C47
HallC3×C7 ⋊ Dic5×C47
SylowC5 ⋊ C7×Dic3×C47
SylowC3 ⋊ C7×Dic5×C47

Subgroups

subgroupG/H
center, hypercenterC2×C7×C47D15
commutator, hypocenterC3×C5C4×C7×C47
FrattiniC2C7×D15×C47
Fitting, socle, prime radicalC2×C3×C5×C7×C47C2
cosocleC2×C3×C5C2×C7×C47
LCSG ▷ C3×C5
UCSC1 ◁ C2×C7×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19740

Conjugacy classes & character table

5922 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 14);