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C2×#26042789 #37551776

order23276
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×#26042789

Splittings

Fitting, socleC2×C232 ⋊ C2×C11
derived, SylowC232 ⋊ C22×C11
Hall#19154122 ⋊ C22
HallC2×C23⋊D23 ⋊ C11

Subgroups

subgroupG/H
center, hypercenterC2#26042789
commutator, cosocle, hypocenterC232C22×C11
FrattiniC1G
Fitting, socleC2×C232C2×C11
LCSG ▷ C232
UCSC1 ◁ C2

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 506

A minimal faithful permutation representation — 2 generators on 48 points:

(2,5,6,13,14,21,16,17,7,18,19,3,4,8,9,20,15,10,22,11,12,23)(25,29,30,42,28,40,41,45,44,38,34,26,27,35,36,32,33,39,46,37,31,43);(1,2,4,7,6,10,12,20,9,15,17,23,19,22,21,13,14,18,16,8,11,5,3)(24,25,28,34,44,35,36,40,27,31,39,45,46,41,38,29,33,42,30,37,43,32,26)(47,48)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23276, 66);