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C23×#1298 #15668917

order2944
nilpotency class3
isoclinismisoclinic class of #327
automorphism?
homologyAbelianization (H1) = C42×C23 · Schur multiplier (H2) = C22

Aliases

direct productC23×#1298

Subgroups

subgroupG/H
centerC2×C4×C23C22⋊C4
commutatorC2×C4C42×C23
Frattini, cosocleC23×C4C22×C23
socleC22×C23#95
prime radicalC24×C23Q8
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C23 ◁ C23×C4×C23 ◁ G

190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 736

A minimal faithful permutation representation — 2 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)(24,25)(26,30)(27,29)(28,31)(32,33,35,40,37,41,36,39)(34,42,43,38,45,46,44,47);(24,26)(25,28,29,30)(27,31)(32,34,36,44,37,45,35,43)(33,38,40,46,41,47,39,42)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#7397, C23×#7433, C2×C23×#1298, …
maximal normal subgroup ofC23×#7397, C23×#7433, C2×C23×#1298, …
maximal quotient ofC23×#7026, C23×#7029, C23×#7038, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 30);