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C5×C7×C97⋊C3 #23779160

order10185
isoclinismisoclinic class of C97⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C97⋊C3
unambiguous semidirect productC97⋊(C3×C5×C7)
unambiguous semidirect product(C5×C97)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C97 ⋊ C3
derived, SylowC97 ⋊ C3×C5×C7
HallC7×C97 ⋊ C3×C5
HallC5×C97 ⋊ C3×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7C97⋊C3
commutator, cosocle, hypocenterC97C3×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C97C3
LCSG ▷ C97
UCSC1 ◁ C5×C7

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C7×C97⋊C3, C5×C7×D97⋊C3, C5×D7×C97⋊C3, …
maximal normal subgroup ofC2×C5×C7×C97⋊C3, C5×C7×D97⋊C3, C5×D7×C97⋊C3, …
maximal quotient ofC2×C5×C7×C97⋊C3, C5×C7×C97⋊C9, C3×C5×C7×C97⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10185, 2);