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C7×#6092 #13089751

order1456
isoclinismisoclinic class of #261
automorphism?
homologyAbelianization (H1) = C7×C16 · Schur multiplier (H2) = C1

Aliases

direct productC7×#6092

Splittings

derived, SylowC13 ⋊ C7×C16
HallC7×C13 ⋊ C16

Subgroups

subgroupG/H
center, hypercenterC4×C7#261
commutator, hypocenterC13C7×C16
FrattiniC4C7×#261
FittingC4×C7×C13C4
socle, prime radicalC2×C7×C13C8
cosocle#1055C2×C7
LCSG ▷ C13
UCSC1 ◁ C4×C7

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 1456

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5,6,7)(9,10,11,13)(12,15,16,20)(14,18,19,17)(21,22,23,26,24,27,29,32,25,28,30,33,31,34,35,36);(8,9,12,15,19,13,17,18,10,14,20,16,11)

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1456, 5);