Finite Group Databasebeta

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C7×#4626 #13051535

order1344
isoclinismisoclinic class of #4626
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C4

Aliases

direct productC7×#4626

Splittings

derivedC42⋊C3 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC7#4626
commutator, hypocenterC42⋊C3C4×C7
FrattiniC23C7×S4
FittingC7×#127D3
socleC22×C7SL(2,ℤ/4)
prime radicalC7×#127⋊C3C2
cosocle#127⋊C3C2×C7
LCSG ▷ C42⋊C3
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 23 points:

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

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 824);