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C2×C5⋊D5×C73 #20300508

order7300
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C73 · Schur multiplier (H2) = C2×C5

Aliases

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

Splittings

Fitting, socleC2×C52×C73 ⋊ C2
derived, SylowC52 ⋊ C22×C73
HallC52×C73 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C73C5⋊D5
commutator, hypocenterC52C22×C73
FrattiniC1G
Fitting, socleC2×C52×C73C2
LCSG ▷ C52
UCSC1 ◁ C2×C73

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2044 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C73×(C5⋊D5)⋊C3, C2×(C5⋊D5)⋊(C73⋊C3), C2×C5⋊D5×C73⋊C3, …
maximal normal subgroup ofC2×C73×(C5⋊D5)⋊C3, C2×(C5⋊D5)⋊(C73⋊C3), C2×C5⋊D5×C73⋊C3, …
maximal quotient ofD3×C5⋊D5×C73, C2×C3×C5⋊D5×C73, C2×C73×C3⋊(C5⋊D5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7300, 47);