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C13×C17×Dic21 #32915422

order18564
automorphism?
homologyAbelianization (H1) = C4×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC13×C17×Dic21
unambiguous semidirect productC3⋊(C13×C17×Dic7)
unambiguous semidirect productC7⋊(Dic3×C13×C17)

Splittings

derived, HallC3×C7 ⋊ C4×C13×C17
HallC3×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ Dic3
HallC3×C13×C17 ⋊ Dic7
HallC3×C7×C17 ⋊ C4×C13
HallC3×C7×C13 ⋊ C4×C17
HallC7×C17 ⋊ Dic3×C13
HallC7×C13 ⋊ Dic3×C17
HallC3×C17 ⋊ C13×Dic7
HallC3×C13 ⋊ C17×Dic7
SylowC7 ⋊ Dic3×C13×C17
SylowC3 ⋊ C13×C17×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C13×C17D21
commutator, hypocenterC3×C7C4×C13×C17
FrattiniC2C13×C17×D21
Fitting, socle, prime radicalC2×C3×C7×C13×C17C2
cosocleC2×C3×C7C2×C13×C17
LCSG ▷ C3×C7
UCSC1 ◁ C2×C13×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18564

Conjugacy classes & character table

5304 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 17);