Finite Group Databasebeta

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C23×C3⋊((C19⋊C3)⋊C4) #30628581

order15732
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊((C19⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C23×(C19⋊C3)⋊C4)
unambiguous semidirect product(C19⋊C3)⋊(Dic3×C23)
unambiguous semidirect productDic57⋊(C3×C23)
unambiguous semidirect product(C23×Dic57)⋊C3

Splittings

derivedC3×C19 ⋊ C3×C4×C23
HallC3×C23×C19⋊C3 ⋊ C4
HallC19×C23 ⋊ C3×Dic3
HallC3×C19⋊C3 ⋊ C4×C23
SylowC19 ⋊ C3×Dic3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊(D19⋊C3)
commutator, hypocenterC3×C19C3×C4×C23
FrattiniC2C23×C3⋊(D19⋊C3)
Fitting, socleC2×C3×C19×C23C2×C3
prime radicalC2×C3×C23×C19⋊C3C2
cosocleC2×C3×C19C2×C3×C23
LCSG ▷ C3×C19
UCSC1 ◁ C2×C23

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5244

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15732, 43);