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C7×#907 #10621304

order672
automorphism?
homologyAbelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C22

Aliases

direct productC7×#907

Splittings

FittingC3×C7×M16 ⋊ C2
HallC3×C7 ⋊ #131
SylowC3 ⋊ C7×#131

Subgroups

subgroupG/H
centerC4×C7C22×D3
commutatorC2×C3C22×C4×C7
FrattiniC4C22×D3×C7
FittingC3×C7×M16C2
socleC2×C3×C7C22×C4
prime radicalC7×#235C2
cosocleC3×C4C23×C7
hypercenterC7×M16D3
hypocenterC3C7×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C7 ◁ C7×M16

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 336

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3,4,5,6,7)(8,9,10)(11,13,14,20,15,19,21,25)(12,17,18,24,16,22,23,26);(12,16)(13,19)(18,23)(20,25);(9,10)(11,12)(13,17)(14,18)(15,16)(19,22)(20,24)(21,23)(25,26)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13053562, #13053567, #13053568, …
maximal normal subgroup of#13053562, #13053567, #13053568, …
maximal quotient ofC7×#4701, C7×#4706, C7×#4708, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 886);