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C2×C7×D5×C73 #23779377

order10220
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C7×C73 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D5×C73
unambiguous semidirect productC5⋊(C22×C7×C73)
unambiguous semidirect product(C2×C5)⋊(C2×C7×C73)

Splittings

Fitting, socleC2×C5×C7×C73 ⋊ C2
derived, SylowC5 ⋊ C22×C7×C73
HallC5×C7×C73 ⋊ C22
HallC5×C73 ⋊ C22×C7
HallC5×C7 ⋊ C22×C73

Subgroups

subgroupG/H
center, hypercenterC2×C7×C73D5
commutator, cosocle, hypocenterC5C22×C7×C73
FrattiniC1G
Fitting, socleC2×C5×C7×C73C2
LCSG ▷ C5
UCSC1 ◁ C2×C7×C73

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4088 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×D5×C73⋊C3, C2×D5×ΓL(1,𝔽8)×C73, C2×D5×#13095275, …
maximal normal subgroup ofC2×C7×D5×C73⋊C3, C2×D5×ΓL(1,𝔽8)×C73, C2×D5×#13095275, …
maximal quotient ofD3×C7×D5×C73, C2×C3×C7×D5×C73, C2×C7×D15×C73

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10220, 32);