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C4×C5×C97⋊C3 #19154128

order5820
isoclinismisoclinic class of C97⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C97⋊C3
unambiguous semidirect product(C4×C97)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C97)⋊C3

Splittings

Fitting, HallC4×C5×C97 ⋊ C3
derived, SylowC97 ⋊ C3×C4×C5
HallC5×C97 ⋊ C3×C4
HallC4×C97 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC4×C5C97⋊C3
commutator, hypocenterC97C3×C4×C5
FrattiniC2C2×C5×C97⋊C3
FittingC4×C5×C97C3
socleC2×C5×C97C2×C3
LCSG ▷ C97
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

700 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×Dic3×C97⋊C3, C3×C4×C5×C97⋊C3, C4×C25×C97⋊C3, …
maximal normal subgroup ofC3×C4×C5×C97⋊C3, C4×C25×C97⋊C3, C4×C52×C97⋊C3
maximal quotient ofC4×C5×C97⋊C9, C5×Dic3×C97⋊C3, C3×C4×C5×C97⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5820, 2);