Finite Group Databasebeta

← Prev (#32915433) Next (#32915435) →

C7×Dic221⋊C3 #32915434

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

Aliases

direct productC7×Dic221⋊C3
unambiguous semidirect productDic221⋊(C3×C7)

Splittings

derived, HallC13×C17 ⋊ C3×C4×C7
HallC7×Dic221 ⋊ C3
HallC7×C17×C13⋊C3 ⋊ C4
HallC7×C13×C17 ⋊ C3×C4
HallDic221 ⋊ C3×C7
HallC17×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ Dic17
HallC7×C17 ⋊ Dic13⋊C3
HallC7×C13 ⋊ C3×Dic17
HallC13⋊C3 ⋊ C7×Dic17
SylowC17 ⋊ C7×Dic13⋊C3
SylowC13 ⋊ C3×C7×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C7C17⋊(D13⋊C3)
commutator, hypocenterC13×C17C3×C4×C7
FrattiniC2C7×C17⋊(D13⋊C3)
Fitting, socleC2×C7×C13×C17C2×C3
prime radicalC2×C7×C17×C13⋊C3C2
cosocleC2×C13×C17C2×C3×C7
LCSG ▷ C13×C17
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6188

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 29);