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C7×C23×C22⋊(C13⋊C3) #38737447

order25116
automorphism?
homologyAbelianization (H1) = C3×C7×C23 · Schur multiplier (H2) = C2

Aliases

direct productC7×C23×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C7×C23×C13⋊C3)
unambiguous semidirect productC13⋊(C7×A4×C23)
unambiguous semidirect product(C22×C23)⋊(C7×C13⋊C3)
unambiguous semidirect product(C13×C23)⋊(C7×A4)

Splittings

Fitting, socle, HallC22×C7×C13×C23 ⋊ C3
derived, HallC22×C13 ⋊ C3×C7×C23
HallC7×C13×C23 ⋊ A4
HallC22×C13×C23 ⋊ C3×C7
HallC22×C7×C23 ⋊ C13⋊C3
HallC22×C7×C13 ⋊ C3×C23
HallC13×C23 ⋊ C7×A4
HallC22×C23 ⋊ C7×C13⋊C3
HallC7×C13 ⋊ A4×C23
HallC22×C7 ⋊ C23×C13⋊C3
SylowC13 ⋊ C7×A4×C23
SylowC22 ⋊ C7×C23×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7×C23C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C7×C23
FrattiniC1G
Fitting, socleC22×C7×C13×C23C3
LCSG ▷ C22×C13
UCSC1 ◁ C7×C23

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8372

Conjugacy classes & character table

3220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 166);