Finite Group Databasebeta

← Prev (#13097539) Next (#13097541) →

C232⋊C3 #13097540

order1587
isoclinismisoclinic class of C232⋊C3
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C23

Aliases

unambiguous semidirect productC232⋊C3

Splittings

Fitting, socle, derived, SylowC232 ⋊ C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC232C3
LCSG ▷ C232
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 69

Polycyclic presentation:

3,23^2|b^a=b^7c^4,c^a=b^3c^15

Conjugacy classes & character table

179 conjugacy classes — view the full character table.

Relationships

derived subgroup of#15691772, C5×#15691772, C3×#20263650, …
maximal subgroup of#15691772, (C23⋊D23)⋊C3, C2×C232⋊C3, …
maximal normal subgroup of#15691772, (C23⋊D23)⋊C3, C2×C232⋊C3, …
maximal quotient ofC2×C232⋊C3, C232⋊C9, C3×C232⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1587, 2);