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C9×C31×Dic23 #38787257

order25668
automorphism?
homologyAbelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C1

Aliases

direct productC9×C31×Dic23
unambiguous semidirect productC23⋊(C4×C9×C31)

Splittings

derived, SylowC23 ⋊ C4×C9×C31
HallC9×C23×C31 ⋊ C4
HallC23×C31 ⋊ C4×C9
HallC9×C23 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC2×C9×C31D23
commutator, hypocenterC23C4×C9×C31
FrattiniC2×C3C3×C31×D23
FittingC2×C9×C23×C31C2
socle, prime radicalC2×C3×C23×C31C2×C3
cosocleC2×C3×C23C2×C3×C31
LCSG ▷ C23
UCSC1 ◁ C2×C9×C31

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25668

Conjugacy classes & character table

7254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 4);