Finite Group Databasebeta

← Prev (#11719664) Next (#11719666) →

C17×C49 #11719665

order833
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C2×C3×C7×C16 (order 672) · Inn(G) = C1 · Out(G) = C2×C3×C7×C16
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC833
abelianC17×C49

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C7×C17
socle, prime radicalC7×C17C7
LCSG ▷ C1
UCSC1 ◁ G

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 833

A minimal faithful permutation representation — 1 generator on 66 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49)(50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66)

Conjugacy classes & character table

833 conjugacy classes. The character table is too large to display.

Relationships

center ofC17×D9×C49, C17×C3⋊D3×C49, C17×AGL(1,𝔽5)×C49, …
derived subgroup ofD833, Dic833, C49⋊#595, …
Fitting subgroup ofC17×D49, D17×C49, D833, …
maximal subgroup ofC17×D49, D17×C49, D833, …
maximal normal subgroup ofC17×D49, D17×C49, D833, …
maximal quotient ofC2×C17×C49, C3×C17×C49, C5×C17×C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(833, 1);