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#49150260

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
HallC13×C19⋊(C52⋊C3) ⋊ C2
HallC5⋊D1235 ⋊ C3
HallC19⋊(C52⋊C3) ⋊ D13
HallC52×C19 ⋊ C3×D13
HallC52×C13 ⋊ D19⋊C3
HallC13×C19 ⋊ (C5⋊D5)⋊C3
SylowC52 ⋊ (C19⋊C3)⋊D13
SylowC19 ⋊ #14519613
SylowC13 ⋊ #15668133

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

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,f^b=f^7

Conjugacy classes & character table

1051 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 86);