Finite Group Databasebeta

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C2×C23×D117 #24924503

order10764
isoclinismisoclinic class of D117
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C23×D117
unambiguous semidirect product(C2×C9)⋊(C23×D13)
unambiguous semidirect product(C2×C13)⋊(D9×C23)

Splittings

FittingC2×C9×C13×C23 ⋊ C2
derived, HallC9×C13 ⋊ C22×C23
HallC9×C13×C23 ⋊ C22
HallC13×C23 ⋊ C2×D9
HallC9×C23 ⋊ C2×D13
SylowC13 ⋊ C2×D9×C23
SylowC9 ⋊ C2×C23×D13

Subgroups

subgroupG/H
center, hypercenterC2×C23D117
commutator, cosocle, hypocenterC9×C13C22×C23
FrattiniC3C2×C23×D39
FittingC2×C9×C13×C23C2
socleC2×C3×C13×C23D3
LCSG ▷ C9×C13
UCSC1 ◁ C2×C23

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10764, 39);