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Cayley diagram

C8×D31 #92468

order496
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

direct productC8×D31

Splittings

FittingC8×C31 ⋊ C2
derived, SylowC31 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC8D31
commutator, hypocenterC31C2×C8
FrattiniC4C2×D31
FittingC8×C31C2
socleC2×C31C2×C4
prime radicalC2×D31C4
cosocleC4×C31C22
LCSG ▷ C31
UCSC1 ◁ C8

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 248

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);(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)(32,33,34,36,35,37,38,39)

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC16×D31, #11758386, C2×C8×D31, …
maximal normal subgroup ofC16×D31, #11758386, C2×C8×D31, …
maximal quotient ofC16×D31, #11758386, C8×Dic31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 3);