Finite Group Databasebeta

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C7×#23900 #13201116

order1792
nilpotency class3
isoclinismisoclinic class of #23900
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C28

Aliases

direct productC7×#23900

Subgroups

subgroupG/H
center, socleC22×C7C2×#120
commutator, Frattini, cosocleC24C24×C7
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C25×C7 ◁ G

3520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 112

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

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

Conjugacy classes & character table

322 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD7×#23900, ΓL(1,𝔽8)×#23900, AGL(1,𝔽7)×#23900
maximal subgroup ofD7×#23900, C7×#347047, ΓL(1,𝔽8)×#23900
maximal normal subgroup ofD7×#23900, C7×#347047, ΓL(1,𝔽8)×#23900

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 16888);