Finite Group Databasebeta

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Cayley diagram

C2×#6433 #90160

order448
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#6433

Splittings

SylowC7 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D7
commutator, cosocleC22×C7C24
FrattiniC22C23×D7
FittingC2×C42×C7C2
socle, prime radicalC23×C7C23
hypercenterC2×C42D7
hypocenterC7C2×#125
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 448

A minimal faithful permutation representation — 4 generators on 25 points:

(1,2)(3,4,6,8,9,7,5)(10,12,13,16)(11,15,14,17)(19,23)(22,25);(11,14)(15,17)(18,20,21,24)(19,22,23,25);(4,5)(6,7)(8,9)(10,11,13,14)(12,15,16,17)(18,19)(20,22)(21,23)(24,25);(1,2)

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11726388, #11726433, #11726444, …
maximal normal subgroup of#11726388, #11726433, #11726444, …
maximal quotient ofC4×#6433, #11730752, #11730755, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 922);