Finite Group Databasebeta

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C2×C7×#1637 #13195705

order1792
nilpotency class3
isoclinismisoclinic class of #1619
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C25

Aliases

direct productC2×C7×#1637

Subgroups

subgroupG/H
center, socleC23×C7#120
commutator, Frattini, cosocleC42C24×C7
prime radicalC22×C7×D4D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 896

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2)(27,28,29,30,31,32,33);(3,4,6,9)(5,7,10,8)(11,12,17,21)(13,22,14,25)(15,20,16,19)(18,24,26,23);(4,7)(5,10)(8,9)(11,13,17,14)(12,18,21,26)(15,24,16,23)(19,25,20,22);(11,14,17,13)(12,18,21,26)(15,23,16,24)(19,25,20,22)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 11477);