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C22×2−1+4×D53 #28297980

order13568
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC22×2−1+4×D53

Splittings

FittingC22×2−1+4×C53 ⋊ C2
SylowC53 ⋊ C23×2−1+4

Subgroups

subgroupG/H
centerC23C24×D53
commutator, cosocleC2×C53C27
FrattiniC2C26×D53
FittingC22×2−1+4×C53C2
socleC23×C53C25
hypercenterC22×2−1+4D53
hypocenterC53C23×2−1+4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×2−1+4

59806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 3392

A minimal faithful permutation representation — 7 generators on 73 points:

(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);(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)(59,65)(63,66)(64,73)(71,72);(58,61,62,70)(59,64,65,73)(60,67,68,69)(63,71,66,72);(58,60,62,68)(59,63,65,66)(61,69,70,67)(64,72,73,71);(58,59)(60,66)(61,64)(62,65)(63,68)(67,72)(69,71)(70,73);(56,57);(54,55)

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1083456);