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C31×#1849 #16841782

order3968
nilpotency class3
automorphism?
homologyAbelianization (H1) = C22×C4×C31 · Schur multiplier (H2) = C2×C4

Aliases

direct productC31×#1849

Subgroups

subgroupG/H
centerC2×C4×C31C2×D4
commutatorC2×C4C22×C4×C31
Frattini, cosocleC22×C4C23×C31
socleC22×C31C2×C4⋊C4
prime radicalC23×C31C2×Q8
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 1984

A minimal faithful permutation representation — 3 generators on 51 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)(33,35)(36,37,40,43,41,44,39,49)(38,45,48,50,46,51,47,42);(36,38,39,47,41,46,40,48)(37,42,43,45,44,50,49,51);(32,33,34,35)(38,46)(42,50)(45,51)(47,48)

Conjugacy classes & character table

992 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC31×#7374, C31×#8916, C31×#10524, …
maximal normal subgroup ofC31×#7374, C31×#8916, C31×#10524, …
maximal quotient ofC31×#8808, C31×#8809, C31×#8810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 581);