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C7×Dic1131 #44539723

order31668
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic1131
unambiguous semidirect productC3⋊(C7×Dic377)

Splittings

derived, HallC3×C13×C29 ⋊ C4×C7
HallC3×C7×C13×C29 ⋊ C4
HallC7×C13×C29 ⋊ Dic3
HallC3×C7×C29 ⋊ Dic13
HallC13×C29 ⋊ C7×Dic3
HallC3×C7×C13 ⋊ Dic29
HallC7×C29 ⋊ Dic39
HallC7×C13 ⋊ Dic87
HallC3×C29 ⋊ C7×Dic13
HallC3×C13 ⋊ C7×Dic29
SylowC29 ⋊ C7×Dic39
HallC3×C7 ⋊ Dic377
SylowC13 ⋊ C7×Dic87
SylowC3 ⋊ C7×Dic377

Subgroups

subgroupG/H
center, hypercenterC2×C7D1131
commutator, hypocenterC3×C13×C29C4×C7
FrattiniC2C7×D1131
Fitting, socle, prime radicalC2×C3×C7×C13×C29C2
cosocleC2×C3×C13×C29C2×C7
LCSG ▷ C3×C13×C29
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31668

Conjugacy classes & character table

7938 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 18);