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C7×#23872 #13201088

order1792
nilpotency class3
isoclinismisoclinic class of #23872
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C27

Aliases

direct productC7×#23872

Subgroups

subgroupG/H
center, socleC2×C7#2403
commutator, Frattini, cosocleC22×C4C24×C7
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G

1790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 23 points:

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

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD7×#23872
maximal subgroup ofD7×#23872
maximal normal subgroup ofD7×#23872

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 16860);