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C2×#26044458 #37555446

order23548
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×#26044458

Splittings

Fitting, socleC2×C292 ⋊ C2×C7
derived, SylowC292 ⋊ C22×C7
Hall#19154635 ⋊ C22
HallC2×C29⋊D29 ⋊ C7

Subgroups

subgroupG/H
center, hypercenterC2#26044458
commutator, cosocle, hypocenterC292C22×C7
FrattiniC1G
Fitting, socleC2×C292C2×C7
LCSG ▷ C292
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 406

A minimal faithful permutation representation — 2 generators on 60 points:

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

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23548, 83);