Finite Group Databasebeta

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Cayley diagram

Q8×D29 #90808

order464
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ8×D29

Splittings

FittingQ8×C29 ⋊ C2
SylowC29 ⋊ C2×Q8

Subgroups

subgroupG/H
center, FrattiniC2C22×D29
commutator, socle, cosocleC2×C29C23
FittingQ8×C29C2
prime radicalC2×D29C22
hypercenterQ8D29
hypocenterC29C2×Q8
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ Q8

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 232

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745225, SD16×D29, #11745277, …
maximal normal subgroup of#11745225, SD16×D29, #11745277, …
maximal quotient of#11745249, #11745250, #11745251, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 41);