Finite Group Databasebeta

← Prev (#15669141) Next (#15669143) →

C2×C23×#330 #15669142

order2944
nilpotency class3
isoclinismisoclinic class of #327
automorphism?
homologyAbelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×C23×#330

Subgroups

subgroupG/H
center, socle, prime radicalC23×C23C22⋊C4
commutatorC2×C4C22×C4×C23
Frattini, cosocleC42C23×C23
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 2944

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C23×#330, C23×#8225, C23×#8227, …
maximal normal subgroup ofC4×C23×#330, C23×#8225, C23×#8227, …
maximal quotient ofC2×C23×#1271, C23×#7568, C23×#7627, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 255);