Finite Group Databasebeta

← Prev (#15670831) Next (#15670833) →

C23×#3213 #15670832

order2944
nilpotency class3
isoclinismisoclinic class of #3192
automorphism?
homologyAbelianization (H1) = C24×C23 · Schur multiplier (H2) = C23×C4

Aliases

direct productC23×#3213

Subgroups

subgroupG/H
center, socleC22×C23C22×D4
commutator, Frattini, cosocleC2×C4C24×C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G

444 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(24,25)(26,30)(27,29)(28,31)(33,36)(34,38)(37,39);(24,26,27,31)(25,28,29,30)(33,37)(36,39);(26,31)(28,30)(32,33)(34,39)(35,37)(36,38);(25,29)(28,30)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23×#9333, C23×#9381, C23×#10004, …
maximal normal subgroup ofC23×#9333, C23×#9381, C23×#10004, …
maximal quotient ofC23×#21808, C23×#21865, C23×#21986, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1945);