Finite Group Databasebeta

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C5×C47×Dic21 #34089459

order19740
automorphism?
homologyAbelianization (H1) = C4×C5×C47 · Schur multiplier (H2) = C1

Aliases

direct productC5×C47×Dic21
unambiguous semidirect productC3⋊(C5×Dic7×C47)
unambiguous semidirect productC7⋊(C5×Dic3×C47)

Splittings

derived, HallC3×C7 ⋊ C4×C5×C47
HallC3×C5×C7×C47 ⋊ C4
HallC5×C7×C47 ⋊ Dic3
HallC3×C7×C47 ⋊ C4×C5
HallC3×C5×C47 ⋊ Dic7
HallC7×C47 ⋊ C5×Dic3
HallC3×C47 ⋊ C5×Dic7
HallC3×C5×C7 ⋊ C4×C47
HallC5×C7 ⋊ Dic3×C47
HallC3×C5 ⋊ Dic7×C47
SylowC7 ⋊ C5×Dic3×C47
SylowC3 ⋊ C5×Dic7×C47

Subgroups

subgroupG/H
center, hypercenterC2×C5×C47D21
commutator, hypocenterC3×C7C4×C5×C47
FrattiniC2C5×D21×C47
Fitting, socle, prime radicalC2×C3×C5×C7×C47C2
cosocleC2×C3×C7C2×C5×C47
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19740

Conjugacy classes & character table

5640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 12);