Finite Group Databasebeta

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C43×#64418 #27162444

order12642
isoclinismisoclinic class of #64418
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×#64418

Splittings

Fitting, socle, HallC72×C43 ⋊ D3
derived, Hall#3862 ⋊ C2×C43
HallC43×#3862 ⋊ C2
SylowC72 ⋊ D3×C43

Subgroups

subgroupG/H
center, hypercenterC43#64418
commutator, cosocle, hypocenter#3862C2×C43
FrattiniC1G
Fitting, socleC72×C43D3
LCSG ▷ #3862
UCSC1 ◁ C43

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 602

A minimal faithful permutation representation — 2 generators on 57 points:

(1,6,12,7,9,2,3,10,13,11,8,4,5,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(3,5,8)(4,6,7)(9,13,12)(10,14,11)

Conjugacy classes & character table

860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD43×#64418, C43×#64418⋊C2, #64418⋊D43, …
maximal normal subgroup ofD43×#64418, C43×#64418⋊C2, #64418⋊D43, …
maximal quotient ofC43×#10596868, C2×C43×#64418, C43×#11725071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12642, 109);