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C29×#2176 #16815890

order3712
nilpotency class4
automorphism?
homologyAbelianization (H1) = C22×C4×C29 · Schur multiplier (H2) = C22

Aliases

direct productC29×#2176

Subgroups

subgroupG/H
center, socle, prime radicalC22×C29C2×D8
commutatorC8C22×C4×C29
Frattini, cosocleC2×C8C23×C29
LCSG ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ C4×C8×C29 ◁ G

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 65
transitive degreeμt(G) = 3712

A minimal faithful permutation representation — 3 generators on 65 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)(30,31,33,32)(34,35)(36,44)(37,48)(38,53)(39,41)(40,45)(42,51)(43,50)(46,64)(47,61)(49,59)(52,60)(54,58)(55,63)(56,65)(57,62);(34,36,39,47)(35,40,41,55)(37,49,52,65)(38,54,50,46)(42,58,57,64)(43,59,53,56)(44,60,61,48)(45,62,63,51);(30,32,33,31)(35,41)(40,55)(42,57)(43,53)(44,61)(48,60)(56,59)(58,64)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#7391, C29×#12066, C29×#12079, …
maximal normal subgroup ofC29×#7391, C29×#12066, C29×#12079, …
maximal quotient ofC29×#12044, C29×#12076, C29×#12085, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 908);