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C47⋊#1181 #19129647

order5452
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC47⋊#1181

Splittings

Fitting, socle, derived, HallC29×C47 ⋊ C4
SylowC47 ⋊ #1181
SylowC29 ⋊ Dic47

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC29×C47C4
LCSG ▷ C29×C47
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,29,47|a^2=b,c^a=c^17,d^a=d^46,c^b=c^28

Conjugacy classes & character table

379 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C47⋊#1181, C3⋊(C47⋊#1181), C5×C47⋊#1181, …
maximal normal subgroup ofC3×C47⋊#1181, C5×C47⋊#1181, C47⋊AGL(1,𝔽29), …
maximal quotient ofC3×C47⋊#1181, C3⋊(C47⋊#1181), C5×C47⋊#1181, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5452, 7);