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C3×C7×Dic221 #32915413

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic221

Splittings

derived, HallC13×C17 ⋊ C3×C4×C7
HallC3×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ C3×C4
HallC3×C13×C17 ⋊ C4×C7
HallC3×C7×C17 ⋊ Dic13
HallC3×C7×C13 ⋊ Dic17
HallC7×C17 ⋊ C3×Dic13
HallC7×C13 ⋊ C3×Dic17
HallC3×C17 ⋊ C7×Dic13
HallC3×C13 ⋊ C7×Dic17
SylowC17 ⋊ C3×C7×Dic13
SylowC13 ⋊ C3×C7×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D221
commutator, hypocenterC13×C17C3×C4×C7
FrattiniC2C3×C7×D221
Fitting, socle, prime radicalC2×C3×C7×C13×C17C2
cosocleC2×C13×C17C2×C3×C7
LCSG ▷ C13×C17
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18564

Conjugacy classes & character table

4704 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 8);