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C5⋊#6732 #11925271

order1200
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊#6732

Splittings

derivedC5×SL(2,𝔽5) ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D5×A5
commutator, hypocenterC5×SL(2,𝔽5)C2
Fitting, socle, cosocleC2×C5C2×A5
LCSG ▷ C5×SL(2,𝔽5)
UCSC1 ◁ C2

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Permutation generators:

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

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΩ+(4,𝔽5), C3×C5⋊#6732, C2×C5⋊#6732, …
maximal normal subgroup ofC3×C5⋊#6732, C2×C5⋊#6732, D5×#6732, …
maximal quotient ofDic5×SL(2,𝔽5), C3×C5⋊#6732, C2×C5⋊#6732

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 481);