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#103×C71 #14555992

order2272
nilpotency class3
isoclinismisoclinic class of D8
automorphism?
homologyAbelianization (H1) = C2×C4×C71 · Schur multiplier (H2) = C2

Aliases

direct product#103×C71

Subgroups

subgroupG/H
center, socle, prime radicalC22×C71D4
commutatorC4C2×C4×C71
Frattini, cosocleC2×C4C22×C71
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C71 ◁ C2×C4×C71 ◁ G

42 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 83
transitive degreeμt(G) = 2272

A minimal faithful permutation representation — 2 generators on 83 points:

(1,2,3,4)(6,9)(7,11)(10,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83);(5,6,8,10)(7,12,11,9)

Conjugacy classes & character table

994 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#103×C71, #416×C71, #417×C71, …
maximal normal subgroup ofC2×#103×C71, #416×C71, #417×C71, …
maximal quotient ofQ8⋊C8×C71, #328×C71, #332×C71, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2272, 10);