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C5×C13×Dic133 #46829115

order34580
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic133
unambiguous semidirect productC7⋊(C5×C13×Dic19)
unambiguous semidirect productC19⋊(C5×C13×Dic7)

Splittings

derived, HallC7×C19 ⋊ C4×C5×C13
HallC5×C7×C13×C19 ⋊ C4
HallC7×C13×C19 ⋊ C4×C5
HallC5×C13×C19 ⋊ Dic7
HallC5×C7×C19 ⋊ C4×C13
HallC5×C7×C13 ⋊ Dic19
HallC13×C19 ⋊ C5×Dic7
HallC5×C19 ⋊ C13×Dic7
HallC7×C13 ⋊ C5×Dic19
HallC5×C7 ⋊ C13×Dic19
SylowC19 ⋊ C5×C13×Dic7
SylowC7 ⋊ C5×C13×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D133
commutator, hypocenterC7×C19C4×C5×C13
FrattiniC2C5×C13×D133
Fitting, socle, prime radicalC2×C5×C7×C13×C19C2
cosocleC2×C7×C19C2×C5×C13
LCSG ▷ C7×C19
UCSC1 ◁ C2×C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34580

Conjugacy classes & character table

8840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 6);