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C7×C17×Dic39 #32915420

order18564
automorphism?
homologyAbelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×Dic39
unambiguous semidirect productC3⋊(C7×C17×Dic13)

Splittings

derived, HallC3×C13 ⋊ C4×C7×C17
HallC3×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ C4×C7
HallC3×C7×C17 ⋊ Dic13
HallC3×C7×C13 ⋊ C4×C17
HallC13×C17 ⋊ C7×Dic3
HallC7×C13 ⋊ Dic3×C17
HallC3×C17 ⋊ C7×Dic13
HallC3×C7 ⋊ C17×Dic13
SylowC13 ⋊ C7×Dic3×C17
SylowC3 ⋊ C7×C17×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C17D39
commutator, hypocenterC3×C13C4×C7×C17
FrattiniC2C7×C17×D39
Fitting, socle, prime radicalC2×C3×C7×C13×C17C2
cosocleC2×C3×C13C2×C7×C17
LCSG ▷ C3×C13
UCSC1 ◁ C2×C7×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18564

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(18564, 15);