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C23×D195 #22582245

order8970
isoclinismisoclinic class of D195
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D195
unambiguous semidirect productC3⋊(C23×D65)
unambiguous semidirect productC5⋊(C23×D39)
unambiguous semidirect productC13⋊(C23×D15)

Splittings

Fitting, socle, HallC3×C5×C13×C23 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C23
HallC5×C13×C23 ⋊ D3
HallC3×C13×C23 ⋊ D5
HallC3×C5×C23 ⋊ D13
HallC13×C23 ⋊ D15
HallC5×C23 ⋊ D39
HallC3×C23 ⋊ D65
HallC5×C13 ⋊ D3×C23
HallC3×C13 ⋊ D5×C23
HallC3×C5 ⋊ C23×D13
SylowC13 ⋊ C23×D15
SylowC5 ⋊ C23×D39
SylowC3 ⋊ C23×D65

Subgroups

subgroupG/H
center, hypercenterC23D195
commutator, hypocenterC3×C5×C13C2×C23
FrattiniC1G
Fitting, socleC3×C5×C13×C23C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2277 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23×D195, C23×D13×D15, D299⋊D15, …
maximal normal subgroup ofD23×D195, C23×D13×D15, D299⋊D15, …
maximal quotient ofC23×Dic195, C2×C23×D195, C23×D585, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8970, 16);