Finite Group Databasebeta

C23×#3566 #15671185

order2944
nilpotency class2
isoclinismisoclinic class of #3532
automorphism?
homologyAbelianization (H1) = C25×C23 · Schur multiplier (H2) = C28

Aliases

direct productC23×#3566

Subgroups

subgroupG/H
center, socleC22×C23C25
commutator, Frattini, cosocleC22C25×C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C23 ◁ G

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 736

A minimal faithful permutation representation — 5 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,31)(26,36)(27,41)(28,44)(32,49)(33,39)(35,48)(37,47)(40,53)(42,50)(43,54)(45,55);(24,25)(26,37)(27,42)(28,34)(29,31)(30,35)(32,36)(33,43)(38,44)(39,41)(40,49)(45,51)(46,48)(47,53)(50,54)(52,55);(24,26,29,40)(25,32,31,47)(27,38,43,34)(28,39,44,50)(30,36,46,53)(33,45,42,55)(35,37,48,49)(41,52,54,51);(24,27)(25,33)(26,38)(28,37)(29,43)(30,41)(31,42)(32,45)(34,40)(35,50)(36,52)(39,48)(44,49)(46,54)(47,55)(51,53);(24,28,30,45)(25,34,35,51)(26,39,36,42)(27,37,41,32)(29,44,46,55)(31,38,48,52)(33,40,50,53)(43,49,54,47)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C23×#3566, C23×#62743, C23×#62755, …
maximal normal subgroup ofC2×C23×#3566, C23×#62743, C23×#62755, …
maximal quotient ofC23×#34387, C23×#34395, C23×#34400, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2298);