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C2×#26044455 #37555443

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

Aliases

direct productC2×#26044455

Splittings

Fitting, socleC2×C292 ⋊ C2×C7
derived, SylowC292 ⋊ C22×C7
Hall#19154634 ⋊ C22
HallC2×C29⋊D29 ⋊ C7

Subgroups

subgroupG/H
center, hypercenterC2#26044455
commutator, cosocle, hypocenterC292C22×C7
FrattiniC1G
Fitting, socleC2×C292C2×C7
LCSG ▷ C292
UCSC1 ◁ C2

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 60
transitive degreeμt(G) = 1682

A minimal faithful permutation representation — 3 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)(31,35,36,50,43,51,57,32,33,40,42,49,55,58)(34,47,48,52,53,44,45,38,39,56,41,54,37,46);(30,31,34,39,49,40,51,42,54,58,56,45,44,35,41,52,33,37,46,48,57,53,50,55,36,43,47,38,32)(59,60);(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)

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, 80);