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C23×#1655 #15669274

order2944
nilpotency class3
isoclinismisoclinic class of #1655
automorphism?
homologyAbelianization (H1) = C23×C23 · Schur multiplier (H2) = C2×C4

Aliases

direct productC23×#1655

Subgroups

subgroupG/H
center, socleC22×C23#120
commutator, Frattini, cosocleC42C23×C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ C42×C23 ◁ G

262 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 736

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#13677, C2×C23×#1655, C23×#18984, …
maximal normal subgroup ofC23×#13677, C2×C23×#1655, C23×#18984, …
maximal quotient ofC23×#7734, C23×#7742, C23×#7745, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 387);