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#34118554

order20202
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, HallC7×C13×C37 ⋊ C2×C3
HallC7×#13089650 ⋊ C2
HallC13×D259 ⋊ C3
Hall#13089650 ⋊ D7
HallD259 ⋊ C13⋊C3
HallC13×C37 ⋊ C3×D7
HallC7×C37 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ D37⋊C3
SylowC37 ⋊ D7×C13⋊C3
SylowC13 ⋊ (C37⋊C3)⋊D7
SylowC7 ⋊ #15668359

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C37C2×C3
LCSG ▷ C7×C13×C37
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 3367

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

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

Polycyclic presentation:

2,3,7,13,37|c^a=c^6,e^a=e^36,d^b=d^3,e^b=e^26

Conjugacy classes & character table

581 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20202, 84);