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D53×#2822 #27590628

order13568
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productD53×#2822

Splittings

FittingC53×#2822 ⋊ C2
SylowC53 ⋊ C2×#2822

Subgroups

subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2822C2
prime radicalC23×D53C24
hypercenter#2822D53
hypocenterC53C2×#2822
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2822

2046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 81
transitive degreeμt(G) = 6784

A minimal faithful permutation representation — 5 generators on 81 points:

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

Conjugacy classes & character table

728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 376104);