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C3×(C43⋊C3)⋊Dic13 #34117489

order20124
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C43⋊C3)⋊Dic13
unambiguous semidirect product(C43⋊C3)⋊(C3×Dic13)

Splittings

derived, HallC13×C43 ⋊ C32×C4
HallC3×C13×C43⋊C3 ⋊ C4
HallDic559 ⋊ C32
HallC3×C43⋊C3 ⋊ Dic13
SylowC43 ⋊ C32×Dic13
SylowC13 ⋊ C3×(C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3(C43⋊C3)⋊D13
commutator, hypocenterC13×C43C32×C4
FrattiniC2C3×(C43⋊C3)⋊D13
Fitting, socleC2×C3×C13×C43C2×C3
prime radicalC2×C3×C13×C43⋊C3C2
cosocleC2×C13×C43C2×C32
LCSG ▷ C13×C43
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 6708

A minimal faithful permutation representation — 2 generators on 63 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,36)(12,26,22,20,16,13)(19,32,34,23,25,37)(21,38,39,30,29,33)(31,41,42,40,35,43)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,60,59,58);(1,2,5,11,19,22,7,6,12,21,31,39,15,26,14,25,35,42,28,37,38,27,18,29,34,36,43,41,32,10,16,24,33,40,30,20,4,8,13,23,17,9,3)(44,45,47,49,51,53,55,56,54,52,50,48,46)(61,62,63)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 92);