Finite Group Databasebeta

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C2×C25×C73⋊C3 #24926526

order10950
isoclinismisoclinic class of C73⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C25×C73⋊C3
unambiguous semidirect product(C2×C73)⋊(C3×C25)
unambiguous semidirect product(C2×C25×C73)⋊C3

Splittings

Fitting, HallC2×C25×C73 ⋊ C3
derived, SylowC73 ⋊ C2×C3×C25
HallC25×C73 ⋊ C2×C3
HallC2×C73 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25C73⋊C3
commutator, hypocenterC73C2×C3×C25
FrattiniC5C2×C5×C73⋊C3
FittingC2×C25×C73C3
socleC2×C5×C73C3×C5
prime radicalC2×C5×C73⋊C3C5
cosocleC5×C73C2×C3×C5
LCSG ▷ C73
UCSC1 ◁ C2×C25

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C25×C73⋊C3, C25×Dic73⋊C3, Dic25×C73⋊C3, …
maximal normal subgroup ofC4×C25×C73⋊C3, C25×Dic73⋊C3, Dic25×C73⋊C3, …
maximal quotient ofC4×C25×C73⋊C3, C22×C25×C73⋊C3, C2×C25×#10620321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10950, 2);