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C5×C7×Dic141 #34089458

order19740
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic141
unambiguous semidirect productC3⋊(C5×C7×Dic47)
unambiguous semidirect productC47⋊(C5×C7×Dic3)

Splittings

derived, HallC3×C47 ⋊ C4×C5×C7
HallC3×C5×C7×C47 ⋊ C4
HallC5×C7×C47 ⋊ Dic3
HallC3×C7×C47 ⋊ C4×C5
HallC3×C5×C47 ⋊ C4×C7
HallC7×C47 ⋊ C5×Dic3
HallC5×C47 ⋊ C7×Dic3
HallC3×C5×C7 ⋊ Dic47
SylowC47 ⋊ C5×C7×Dic3
HallC3×C7 ⋊ C5×Dic47
HallC3×C5 ⋊ C7×Dic47
SylowC3 ⋊ C5×C7×Dic47

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D141
commutator, hypocenterC3×C47C4×C5×C7
FrattiniC2C5×C7×D141
Fitting, socle, prime radicalC2×C3×C5×C7×C47C2
cosocleC2×C3×C47C2×C5×C7
LCSG ▷ C3×C47
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19740

Conjugacy classes & character table

5040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 11);