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C3×C7×Dic235 #34089454

order19740
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic235
unambiguous semidirect productC47⋊(C3×C7×Dic5)

Splittings

derived, HallC5×C47 ⋊ C3×C4×C7
HallC3×C5×C7×C47 ⋊ C4
HallC5×C7×C47 ⋊ C3×C4
HallC3×C7×C47 ⋊ Dic5
HallC3×C5×C47 ⋊ C4×C7
HallC7×C47 ⋊ C3×Dic5
HallC3×C47 ⋊ C7×Dic5
HallC3×C5×C7 ⋊ Dic47
SylowC47 ⋊ C3×C7×Dic5
HallC5×C7 ⋊ C3×Dic47
HallC3×C5 ⋊ C7×Dic47
SylowC5 ⋊ C3×C7×Dic47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D235
commutator, hypocenterC5×C47C3×C4×C7
FrattiniC2C3×C7×D235
Fitting, socle, prime radicalC2×C3×C5×C7×C47C2
cosocleC2×C5×C47C2×C3×C7
LCSG ▷ C5×C47
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19740

Conjugacy classes & character table

4998 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19740, 7);