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D377 #10625366

order754
isoclinismisoclinic class of D377
automorphismAut(G) order 126672
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD377
unambiguous semidirect productC13⋊D29
unambiguous semidirect productC29⋊D13

Splittings

Fitting, socle, derived, HallC13×C29 ⋊ C2
SylowC29 ⋊ D13
SylowC13 ⋊ D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C29C2
LCSG ▷ C13×C29
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 377

A minimal faithful permutation representation — 2 generators on 42 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)

Polycyclic presentation:

2,13,29|b^a=b^12,c^a=c^28

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13094087, #13094088, D13×D29, …
maximal normal subgroup of#13094087, #13094088, D13×D29, …
maximal quotient ofDic377, C2×D377, C3×D377, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(754, 3);