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C5×C23×C31⋊C3 #24924121

order10695
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×C31⋊C3
unambiguous semidirect product(C5×C31)⋊(C3×C23)
unambiguous semidirect product(C5×C23×C31)⋊C3

Splittings

Fitting, socle, HallC5×C23×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C5×C23
HallC23×C31 ⋊ C3×C5
HallC5×C31 ⋊ C3×C23

Subgroups

subgroupG/H
center, hypercenterC5×C23C31⋊C3
commutator, cosocle, hypocenterC31C3×C5×C23
FrattiniC1G
Fitting, socleC5×C23×C31C3
LCSG ▷ C31
UCSC1 ◁ C5×C23

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1495 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C23×C31⋊C3, C5×C23×D31⋊C3, C5×D23×C31⋊C3, …
maximal normal subgroup ofC2×C5×C23×C31⋊C3, C5×C23×D31⋊C3, C5×D23×C31⋊C3, …
maximal quotient ofC2×C5×C23×C31⋊C3, C5×C23×C31⋊C9, C3×C5×C23×C31⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10695, 3);