Finite Group Databasebeta

← Prev (#89676) Next (#89678) →

Cayley diagram

C2×Dic56 #89677

order448
isoclinismisoclinic class of D112
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic56

Splittings

SylowC7 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D56
commutator, cosocleC7×C8C23
FrattiniC8C22×D7
FittingC2×C7×C16C2
socle, prime radicalC22×C7D8
hypercenterC2×C16D7
hypocenterC7C2×Q32
LCSG ▷ C7×C8 ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 448

A minimal faithful permutation representation — 3 generators on 41 points:

(3,4,6,8,9,7,5)(10,12,21,37,14,23,27,29,15,24,32,41,26,38,13,22)(11,16,25,35,18,30,33,36,19,31,40,39,28,34,17,20);(1,2)(4,5)(6,7)(8,9)(10,11,15,19)(12,20,24,36)(13,25,27,40)(14,28,26,18)(16,29,31,22)(17,32,33,21)(23,39,38,35)(30,37,34,41);(1,2)

Conjugacy classes & character table

118 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11725384, #11725390, #11725403, …
maximal normal subgroup of#11725384, #11725390, #11725403, …
maximal quotient of#11726798, C4×Dic56, #11726819, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 439);