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C7×C13×Dic51 #32915419

order18564
automorphism?
homologyAbelianization (H1) = C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×Dic51
unambiguous semidirect productC3⋊(C7×C13×Dic17)

Splittings

derived, HallC3×C17 ⋊ C4×C7×C13
HallC3×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ C4×C7
HallC3×C7×C17 ⋊ C4×C13
HallC3×C7×C13 ⋊ Dic17
HallC13×C17 ⋊ C7×Dic3
HallC7×C17 ⋊ Dic3×C13
HallC3×C13 ⋊ C7×Dic17
HallC3×C7 ⋊ C13×Dic17
SylowC17 ⋊ C7×Dic3×C13
SylowC3 ⋊ C7×C13×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13D51
commutator, hypocenterC3×C17C4×C7×C13
FrattiniC2C7×C13×D51
Fitting, socle, prime radicalC2×C3×C7×C13×C17C2
cosocleC2×C3×C17C2×C7×C13
LCSG ▷ C3×C17
UCSC1 ◁ C2×C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18564

Conjugacy classes & character table

4914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 14);