Finite Group Databasebeta

C31×#1373 #16841306

order3968
nilpotency class4
isoclinismisoclinic class of D16
automorphism?
homologyAbelianization (H1) = C2×C8×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×#1373

Subgroups

subgroupG/H
centerC8×C31D8
commutatorC8C2×C8×C31
Frattini, cosocleC4×C8C22×C31
socleC2×C31#335
prime radicalC22×C31#108
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C31 ◁ C2×C8×C31 ◁ C4×C8×C31 ◁ G

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 992

A minimal faithful permutation representation — 2 generators on 63 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)(32,33,36,41,37,43,35,51,38,44,46,40,52,42,53,58)(34,45,48,55,49,60,47,39,50,54,61,56,62,59,63,57);(32,34,46,61,37,49,53,63,38,50,36,48,52,62,35,47)(33,39,51,59,42,55,41,54,44,57,58,60,43,56,40,45)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC31×#7387, C31×#7388, C31×#7447, …
maximal normal subgroup ofC31×#7387, C31×#7388, C31×#7447, …
maximal quotient ofC31×#7100, C31×#7101, C31×#7160, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 105);