Finite Group Databasebeta

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C7×C17×Dic69 #45659246

order32844
automorphism?
homologyAbelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×Dic69
unambiguous semidirect productC3⋊(C7×C17×Dic23)
unambiguous semidirect productC23⋊(C7×Dic3×C17)

Splittings

derived, HallC3×C23 ⋊ C4×C7×C17
HallC3×C7×C17×C23 ⋊ C4
HallC7×C17×C23 ⋊ Dic3
HallC3×C17×C23 ⋊ C4×C7
HallC3×C7×C23 ⋊ C4×C17
HallC17×C23 ⋊ C7×Dic3
HallC3×C7×C17 ⋊ Dic23
HallC7×C23 ⋊ Dic3×C17
HallC3×C17 ⋊ C7×Dic23
SylowC23 ⋊ C7×Dic3×C17
HallC3×C7 ⋊ C17×Dic23
SylowC3 ⋊ C7×C17×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C17D69
commutator, hypocenterC3×C23C4×C7×C17
FrattiniC2C7×C17×D69
Fitting, socle, prime radicalC2×C3×C7×C17×C23C2
cosocleC2×C3×C23C2×C7×C17
LCSG ▷ C3×C23
UCSC1 ◁ C2×C7×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32844

Conjugacy classes & character table

8568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 11);