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C5×C5⋊(#66524⋊C2) #30659237

order16650
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C5⋊(#66524⋊C2)
unambiguous semidirect productC5⋊(C5×#66524⋊C2)
unambiguous semidirect product#66524⋊(C5×D5)

Splittings

derivedC5×C37 ⋊ C2×C5×C9
HallC52×#66524 ⋊ C2
HallC5×D185 ⋊ C9
HallC52×C37 ⋊ C2×C9
Hall#66524 ⋊ C5×D5
SylowC37 ⋊ C5×C9×D5
SylowC52 ⋊ #66524⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C5C5⋊(D37⋊C3)
commutator, hypocenterC5×C37C2×C5×C9
FrattiniC3C5×C5⋊(D37⋊C3)
Fitting, socleC3×C52×C37C2×C3
prime radicalC3×C5×D185C3
cosocleC3×C5×C37C2×C3×C5
LCSG ▷ C5×C37
UCSC1 ◁ C3×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3330

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#20269018, C5×#20269019, C5×D5×#66524⋊C2, …
maximal normal subgroup ofC5×#20269018, C5×#20269019, C5×D5×#66524⋊C2, …
maximal quotient ofC5×#20269007, C2×C5×C5⋊(#66524⋊C2)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 39);