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Cayley diagram

C3⋊#1181 #66827

order348
isoclinismisoclinic class of C3⋊#1181
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊#1181

Splittings

Fitting, socle, derived, HallC3×C29 ⋊ C4
SylowC29 ⋊ Dic3
SylowC3 ⋊ #1181

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C29C4
prime radical, cosocleC3×D29C2
LCSG ▷ C3×C29
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 87

A minimal faithful permutation representation — 2 generators on 32 points:

(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,26)(14,19,21,23)(16,24,25,20)(22,27,28,29)(31,32);(1,2,5,10,19,8,16,26,29,28,21,13,6,11,20,24,12,3,7,14,22,27,17,25,15,23,18,9,4)(30,31,32)

Polycyclic presentation:

2^2,3,29|a^2=b,c^a=c^2,d^a=d^17,d^b=d^28

Conjugacy classes & character table

27 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#1181, C2×C3⋊#1181, C9⋊#1181, …
maximal normal subgroup ofD3×#1181, C2×C3⋊#1181, C3×C3⋊#1181, …
maximal quotient ofC3⋊#6599, C2×C3⋊#1181, C9⋊#1181, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(348, 6);