Finite Group Databasebeta

← Prev (#38787268) Next (#38787270) →

C2×C23⋊(D31⋊C9) #38787269

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

Aliases

direct productC2×C23⋊(D31⋊C9)
unambiguous semidirect product(C2×C23)⋊(D31⋊C9)
unambiguous semidirect product(C2×C31⋊C9)⋊D23
unambiguous semidirect product(C2×D713)⋊C9

Splittings

derived, HallC23×C31 ⋊ C22×C9
HallC23×C31⋊C9 ⋊ C22
HallC2×D713 ⋊ C9
HallC31⋊C9 ⋊ C2×D23
SylowC31 ⋊ C2×C9×D23
SylowC23 ⋊ C2×D31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C23⋊(D31⋊C3)
commutator, hypocenterC23×C31C22×C9
FrattiniC3C2×C23⋊(D31⋊C3)
Fitting, socleC2×C3×C23×C31C2×C3
prime radicalC2×C3×D713C3
cosocleC3×C23×C31C22×C3
LCSG ▷ C23×C31
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12834

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 16);