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Cayley diagram

D7×2−1+4 #90619

order448
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD7×2−1+4

Splittings

FittingC7×2−1+4 ⋊ C2
SylowC7 ⋊ C2×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2C24×D7
commutator, socle, cosocleC2×C7C25
FittingC7×2−1+4C2
hypercenter2−1+4D7
hypocenterC7C2×2−1+4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ 2−1+4

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 112

A minimal faithful permutation representation — 5 generators on 23 points:

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

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×#454, #11737730, D7×#456, …
maximal normal subgroup ofD7×#454, #11737730, D7×#456, …
maximal quotient of#11742941, #11742943, #11742944, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1381);