Finite Group Databasebeta

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C2×C23×D31⋊C9 #38787268

order25668
automorphism?
homologyAbelianization (H1) = C22×C9×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D31⋊C9
unambiguous semidirect productD31⋊(C2×C9×C23)
unambiguous semidirect product(C2×D31)⋊(C9×C23)
unambiguous semidirect product(C31⋊C9)⋊(C22×C23)
unambiguous semidirect product(C2×C31⋊C9)⋊(C2×C23)
unambiguous semidirect product(C2×C23×D31)⋊C9

Splittings

derived, SylowC31 ⋊ C22×C9×C23
HallC23×C31⋊C9 ⋊ C22
HallC2×C23×D31 ⋊ C9
HallC23×C31 ⋊ C22×C9
HallC31⋊C9 ⋊ C22×C23
HallC2×D31 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D31⋊C3
commutator, hypocenterC31C22×C9×C23
FrattiniC3C2×C23×D31⋊C3
Fitting, socleC2×C3×C23×C31C2×C3
prime radicalC2×C3×C23×D31C3
cosocleC3×C31C22×C3×C23
LCSG ▷ C31
UCSC1 ◁ C2×C3×C23

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12834

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 15);