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C13×C23×D7⋊C9 #49179151

order37674
automorphism?
homologyAbelianization (H1) = C2×C9×C13×C23 · Schur multiplier (H2) = C1

Aliases

direct productC13×C23×D7⋊C9
unambiguous semidirect productD7⋊(C9×C13×C23)
unambiguous semidirect product(C7⋊C9)⋊(C2×C13×C23)
unambiguous semidirect product(D7×C23)⋊(C9×C13)

Splittings

derived, SylowC7 ⋊ C2×C9×C13×C23
HallC13×C23×C7⋊C9 ⋊ C2
HallC13×D7×C23 ⋊ C9
HallC7×C13×C23 ⋊ C2×C9
HallC23×C7⋊C9 ⋊ C2×C13
HallC13×C7⋊C9 ⋊ C2×C23
HallD7×C23 ⋊ C9×C13
HallC13×D7 ⋊ C9×C23
HallC7×C23 ⋊ C2×C9×C13
HallC7×C13 ⋊ C2×C9×C23
HallC7⋊C9 ⋊ C2×C13×C23
HallD7 ⋊ C9×C13×C23

Subgroups

subgroupG/H
center, hypercenterC3×C13×C23AGL(1,𝔽7)
commutator, hypocenterC7C2×C9×C13×C23
FrattiniC3C13×C23×AGL(1,𝔽7)
Fitting, socleC3×C7×C13×C23C2×C3
prime radicalC3×C13×D7×C23C3
cosocleC3×C7C2×C3×C13×C23
LCSG ▷ C7
UCSC1 ◁ C3×C13×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18837

Conjugacy classes & character table

6279 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37674, 34);