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2−1+4⋊A5 #14515306

order1920
isoclinismisoclinic class of 2−1+4⋊A5
automorphismAut(G) = #11757163⋊C2 (order 1920) · Inn(G) = #11757163 · Out(G) = C2
homologyAbelianization (H1) = C1 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product2−1+4⋊A5

Splittings

Fitting2−1+4 ⋊ A5

Subgroups

subgroupG/H
center, Frattini, socle, hypercenterC2#11757163
commutator, hypocenterGC1
Fitting, cosocle2−1+4A5
LCSG
UCSC1 ◁ C2

86 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

16 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC2×2−1+4⋊A5
maximal subgroup of#72209926, #72213587, #72227581, …
maximal normal subgroup of#72209926, C2×2−1+4⋊A5
maximal quotient of#72209606, #72213587, #72226658, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 241004);