Finite Group Databasebeta

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C3×Dic1547 #32915417

order18564
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic1547

Splittings

derived, HallC7×C13×C17 ⋊ C3×C4
HallC3×C7×C13×C17 ⋊ C4
HallC3×C13×C17 ⋊ Dic7
HallC3×C7×C17 ⋊ Dic13
HallC3×C7×C13 ⋊ Dic17
HallC13×C17 ⋊ C3×Dic7
HallC7×C17 ⋊ C3×Dic13
HallC7×C13 ⋊ C3×Dic17
HallC3×C17 ⋊ Dic91
HallC3×C13 ⋊ Dic119
HallC3×C7 ⋊ Dic221
SylowC17 ⋊ C3×Dic91
SylowC13 ⋊ C3×Dic119
SylowC7 ⋊ C3×Dic221

Subgroups

subgroupG/H
center, hypercenterC2×C3D1547
commutator, hypocenterC7×C13×C17C3×C4
FrattiniC2C3×D1547
Fitting, socle, prime radicalC2×C3×C7×C13×C17C2
cosocleC2×C7×C13×C17C2×C3
LCSG ▷ C7×C13×C17
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18564

Conjugacy classes & character table

4650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 12);