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C2×C23×#479 #15670694

order2944
nilpotency class3
isoclinismisoclinic class of #447
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C24

Aliases

direct productC2×C23×#479

Subgroups

subgroupG/H
center, socle, prime radicalC23×C23C2×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 4 generators on 49 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(3,4,6,8)(5,9,10,7)(11,12,14,16)(13,19,20,26)(15,23,22,18)(17,24,25,21);(3,5,6,10)(4,7,8,9)(12,16)(17,25)(18,23)(19,26);(11,13,14,20)(12,17,16,25)(15,24,22,21)(18,26,23,19)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9246, C4×C23×#479, C23×#21618, …
maximal normal subgroup ofC23×#9246, C4×C23×#479, C23×#21618, …
maximal quotient ofC2×C23×#1805, C2×C23×#1863, C2×C23×#1865, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1807);