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C3×Dic1645 #34089456

order19740
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic1645
unambiguous semidirect productC47⋊(C3×Dic35)

Splittings

derived, HallC5×C7×C47 ⋊ C3×C4
HallC3×C5×C7×C47 ⋊ C4
HallC3×C7×C47 ⋊ Dic5
HallC3×C5×C47 ⋊ Dic7
HallC7×C47 ⋊ C3×Dic5
HallC5×C47 ⋊ C3×Dic7
HallC3×C47 ⋊ Dic35
HallC3×C5×C7 ⋊ Dic47
SylowC47 ⋊ C3×Dic35
HallC5×C7 ⋊ C3×Dic47
HallC3×C7 ⋊ Dic235
HallC3×C5 ⋊ Dic329
SylowC7 ⋊ C3×Dic235
SylowC5 ⋊ C3×Dic329

Subgroups

subgroupG/H
center, hypercenterC2×C3D1645
commutator, hypocenterC5×C7×C47C3×C4
FrattiniC2C3×D1645
Fitting, socle, prime radicalC2×C3×C5×C7×C47C2
cosocleC2×C5×C7×C47C2×C3
LCSG ▷ C5×C7×C47
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19740

Conjugacy classes & character table

4944 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 9);