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C3⋊#6732 #10623949

order720
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊#6732

Splittings

derivedC3×SL(2,𝔽5) ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D3×A5
commutator, hypocenterC3×SL(2,𝔽5)C2
Fitting, socle, cosocleC2×C3C2×A5
LCSG ▷ C3×SL(2,𝔽5)
UCSC1 ◁ C2

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Permutation generators:

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

Conjugacy classes & character table

27 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13088291, #13088293, #13088295, …
maximal normal subgroup of#13088291, #13088293, #13088295, …
maximal quotient ofDic3×SL(2,𝔽5), C2×C3⋊#6732, #72228179, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 418);