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C3×C23⋊((C19⋊C3)⋊C4) #30628579

order15732
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23⋊((C19⋊C3)⋊C4)
unambiguous semidirect productC23⋊(C3×(C19⋊C3)⋊C4)
unambiguous semidirect product(C19⋊C3)⋊(C3×Dic23)
unambiguous semidirect productDic437⋊C32
unambiguous semidirect product(C3×Dic437)⋊C3

Splittings

derived, HallC19×C23 ⋊ C32×C4
HallC3×C23×C19⋊C3 ⋊ C4
HallDic437 ⋊ C32
HallC3×C19⋊C3 ⋊ Dic23
SylowC23 ⋊ C3×(C19⋊C3)⋊C4
SylowC19 ⋊ C32×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3C23⋊(D19⋊C3)
commutator, hypocenterC19×C23C32×C4
FrattiniC2C3×C23⋊(D19⋊C3)
Fitting, socleC2×C3×C19×C23C2×C3
prime radicalC2×C3×C23×C19⋊C3C2
cosocleC2×C19×C23C2×C32
LCSG ▷ C19×C23
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5244

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 41);