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(C199⋊C3)⋊AGL(1,𝔽5) #26045901

order11940
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C199⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C199⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, derived, HallC5×C199 ⋊ C3×C4
HallC199⋊AGL(1,𝔽5) ⋊ C3
HallC5×C199⋊C3 ⋊ C4
HallC199⋊C3 ⋊ AGL(1,𝔽5)
SylowC199 ⋊ C3×AGL(1,𝔽5)
SylowC5 ⋊ (C199⋊C3)⋊C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C199C3×C4
prime radicalD5×C199⋊C3C2
cosocleD5×C199C2×C3
LCSG ▷ C5×C199
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,2,5,199|a^2=c,d^a=d^2,e^a=e^198,e^b=e^92,d^c=d^4

Conjugacy classes & character table

147 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13184226⋊AGL(1,𝔽5), C3×(C199⋊C3)⋊AGL(1,𝔽5), C3⋊((C199⋊C3)⋊AGL(1,𝔽5))
maximal normal subgroup of#13184226⋊AGL(1,𝔽5), C3×(C199⋊C3)⋊AGL(1,𝔽5)
maximal quotient of#13184224⋊AGL(1,𝔽5), C3×(C199⋊C3)⋊AGL(1,𝔽5), C3⋊((C199⋊C3)⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11940, 14);