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C3×AGL(1,𝔽5)×C199 #26045907

order11940
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C3×C4×C199 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C199

Splittings

Fitting, socle, HallC3×C5×C199 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C199
HallC5×C199 ⋊ C3×C4
HallC3×C5 ⋊ C4×C199

Subgroups

subgroupG/H
center, hypercenterC3×C199AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C199
FrattiniC1G
Fitting, socleC3×C5×C199C4
prime radicalC3×D5×C199C2
cosocleD5C2×C3×C199
LCSG ▷ C5
UCSC1 ◁ C3×C199

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2985 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#13184224, C9×AGL(1,𝔽5)×C199, C3×AGL(1,𝔽5)×C199⋊C3, …
maximal normal subgroup ofAGL(1,𝔽5)×#13184224, C9×AGL(1,𝔽5)×C199, C3×AGL(1,𝔽5)×C199⋊C3, …
maximal quotient ofC9×AGL(1,𝔽5)×C199, C32×AGL(1,𝔽5)×C199, C3×ΓL(1,𝔽16)×C199

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11940, 20);