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C23×#1708 #15669327

order2944
nilpotency class3
isoclinismisoclinic class of #1705
automorphism?
homologyAbelianization (H1) = C23×C23 · Schur multiplier (H2) = C8

Aliases

direct productC23×#1708

Subgroups

subgroupG/H
center, socleC22×C23#127
commutator, Frattini, cosocleC42C23×C23
prime radicalC23×#127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C42×C23 ◁ G

190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#7536, C23×#12365, C2×C23×#1708, …
maximal normal subgroup ofC23×#7536, C23×#12365, C2×C23×#1708, …
maximal quotient ofC23×#8815, C23×#9819, C23×#9820, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 440);