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Cayley diagram

Q8×D31 #92498

order496
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ8×D31

Splittings

FittingQ8×C31 ⋊ C2
SylowC31 ⋊ C2×Q8

Subgroups

subgroupG/H
center, FrattiniC2C22×D31
commutator, socle, cosocleC2×C31C23
FittingQ8×C31C2
prime radicalC2×D31C22
hypercenterQ8D31
hypocenterC31C2×Q8
LCSG ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ Q8

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(32,34,35,39)(33,36,37,38);(32,33,35,37)(34,38,39,36)

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofSD16×D31, #11758492, Q16×D31, …
maximal normal subgroup ofSD16×D31, #11758492, Q16×D31, …
maximal quotient of#11758464, #11758465, #11758466, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 33);