Finite Group Databasebeta

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C23×Dic31⋊C9 #38787263

order25668
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×Dic31⋊C9
unambiguous semidirect productDic31⋊(C9×C23)
unambiguous semidirect product(C31⋊C9)⋊(C4×C23)
unambiguous semidirect product(C23×Dic31)⋊C9

Splittings

derived, SylowC31 ⋊ C4×C9×C23
HallC23×C31⋊C9 ⋊ C4
HallC23×Dic31 ⋊ C9
HallC23×C31 ⋊ C4×C9
HallC31⋊C9 ⋊ C4×C23
HallDic31 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D31⋊C3
commutator, hypocenterC31C4×C9×C23
FrattiniC2×C3C23×D31⋊C3
Fitting, socle, prime radicalC2×C3×C23×C31C2×C3
cosocleC2×C3×C31C2×C3×C23
LCSG ▷ C31
UCSC1 ◁ C2×C3×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25668

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, 10);