Finite Group Databasebeta

← Prev (#44394009) Next (#44394011) →

C3×D4823 #44394010

order28938
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4823
unambiguous semidirect productC53⋊(C3×D91)

Splittings

Fitting, socle, HallC3×C7×C13×C53 ⋊ C2
derived, HallC7×C13×C53 ⋊ C2×C3
HallC3×C13×C53 ⋊ D7
HallC3×C7×C53 ⋊ D13
HallC13×C53 ⋊ C3×D7
HallC7×C53 ⋊ C3×D13
HallC3×C7×C13 ⋊ D53
HallC3×C53 ⋊ D91
HallC7×C13 ⋊ C3×D53
SylowC53 ⋊ C3×D91
HallC3×C13 ⋊ D371
HallC3×C7 ⋊ D689
SylowC13 ⋊ C3×D371
SylowC7 ⋊ C3×D689

Subgroups

subgroupG/H
center, hypercenterC3D4823
commutator, cosocle, hypocenterC7×C13×C53C2×C3
FrattiniC1G
Fitting, socleC3×C7×C13×C53C2
LCSG ▷ C7×C13×C53
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 76
transitive degreeμt(G) = 14469

A minimal faithful permutation representation — 2 generators on 76 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76);(5,10)(6,9)(7,8)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(25,76)(26,75)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)(33,68)(34,67)(35,66)(36,65)(37,64)(38,63)(39,62)(40,61)(41,60)(42,59)(43,58)(44,57)(45,56)(46,55)(47,54)(48,53)(49,52)(50,51)

Conjugacy classes & character table

7239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28938, 14);