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Cayley diagram

D4×D31 #92496

order496
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD4×D31

Splittings

FittingD4×C31 ⋊ C2
SylowC31 ⋊ C2×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×D31
commutator, socle, cosocleC2×C31C23
FittingD4×C31C2
hypercenterD4D31
hypocenterC31C2×D4
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ D4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 124

A minimal faithful permutation representation — 3 generators on 35 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)(33,35);(32,33)(34,35)

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×D31, #11758488, SD16×D31, …
maximal normal subgroup ofD8×D31, #11758488, SD16×D31, …
maximal quotient of#11758455, C22⋊C4×D31, (C22⋊D31)⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 31);