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C5×D5×#4296 #22555530

order8550
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×D5×#4296
unambiguous semidirect productC5⋊(C2×C5×#4296)

Splittings

Fitting, socle, HallC52×C19 ⋊ C2×C9
derivedC5×C19 ⋊ C2×C5×C9
HallC52×#4296 ⋊ C2
HallC5×D5×C19 ⋊ C9
SylowC52 ⋊ C2×#4296
SylowC19 ⋊ C5×C9×D5

Subgroups

subgroupG/H
center, hypercenterC5D5×#4296
commutator, hypocenterC5×C19C2×C5×C9
FrattiniC1G
Fitting, socleC52×C19C2×C9
LCSG ▷ C5×C19
UCSC1 ◁ C5

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#4296⋊AGL(1,𝔽5), C5×AGL(1,𝔽5)×#4296, C5×D5×AGL(1,𝔽19), …
maximal normal subgroup ofC5×#4296⋊AGL(1,𝔽5), C5×AGL(1,𝔽5)×#4296, C5×D5×AGL(1,𝔽19), …
maximal quotient ofC5×Dic5×#4296, C2×C5×D5×#4296

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8550, 68);