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C2×#26044459 #37555447

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

Aliases

direct productC2×#26044459

Splittings

Fitting, socleC2×C292 ⋊ C2×C7
derived, SylowC292 ⋊ C22×C7
Hall#19154636 ⋊ C22
HallC2×C29⋊D29 ⋊ C7

Subgroups

subgroupG/H
center, hypercenterC2#26044459
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)(31,35,36,49,42,57,53,32,33,41,43,51,52,48)(34,45,46,50,58,47,44,38,39,54,55,56,40,37);(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)(30,31,34,40,48,49,51,33,37,41,50,46,56,57,39,45,52,58,54,55,36,44,35,42,43,53,47,38,32)(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, 84);