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#49150252

order37050
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, HallC52×C13×C19 ⋊ C2×C3
HallC19×C13⋊(C52⋊C3) ⋊ C2
HallC5⋊D1235 ⋊ C3
HallC13⋊(C52⋊C3) ⋊ D19
HallC52×C19 ⋊ D13⋊C3
HallC52×C13 ⋊ C3×D19
HallC13×C19 ⋊ (C5⋊D5)⋊C3
SylowC52 ⋊ (C13⋊C3)⋊D19
SylowC19 ⋊ #14519615
SylowC13 ⋊ #15668135

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C13×C19C2×C3
LCSG ▷ C52×C13×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 3705

A minimal faithful permutation representation — 2 generators on 47 points:

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

Polycyclic presentation:

2,3,5^2,13,19|c^a=c^4,d^a=d^4,e^a=e^12,f^a=f^18,c^b=cd,d^b=c^2d^3,e^b=e^3

Conjugacy classes & character table

1059 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 78);