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C23×C11×Q32 #14639820

order2816
nilpotency class4
isoclinismisoclinic class of D16
automorphism?
homologyAbelianization (H1) = C25×C11 · Schur multiplier (H2) = C29

Aliases

direct productC23×C11×Q32

Subgroups

subgroupG/H
center, socle, prime radicalC24×C11D8
commutator, Frattini, cosocleC8C25×C11
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 2816

A minimal faithful permutation representation — 5 generators on 49 points:

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

Conjugacy classes & character table

968 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 55615);