Finite Group Databasebeta

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Cayley diagram

#41×Dic7 #90517

order448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#41×Dic7

Splittings

SylowC7 ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×D7
commutatorC2×C7C23×C4
FrattiniC22C23×D7
Fitting, prime radicalC2×C7×#41C2
socle, cosocleC22×C7C24
hypercenterC2×#41D7
hypocenterC7C4×#41
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C2×#41

310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 224

A minimal faithful permutation representation — 4 generators on 19 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11727793, #11727885, Dic7×#104, …
maximal normal subgroup of#11727793, #11727885, Dic7×#104, …
maximal quotient ofDic7×#117, #11739672, #11739674, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1279);