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Cayley diagram

C4×Dic31 #92475

order496
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C4

Aliases

direct productC4×Dic31
unambiguous semidirect productC31⋊C42

Splittings

derived, SylowC31 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC2×C4D31
commutator, hypocenterC31C42
FrattiniC22C2×D31
FittingC2×C4×C31C2
socle, prime radical, cosocleC22×C31C22
LCSG ▷ C31
UCSC1 ◁ C2×C4

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 496

A minimal faithful permutation representation — 2 generators on 39 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×Dic31, Dic31⋊C8, #11758403, …
maximal normal subgroup ofC8×Dic31, Dic31⋊C8, #11758403, …
maximal quotient ofC4×C31⋊C8, #11758391, C8×Dic31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 10);