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Cayley diagram

D148 #64441

order296
isoclinismisoclinic class of Dic74
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD148
unambiguous semidirect productC4⋊D37

Splittings

FittingC4×C37 ⋊ C2
SylowC37 ⋊ D4

Subgroups

subgroupG/H
center, FrattiniC2C2×D37
commutator, socle, cosocleC2×C37C22
FittingC4×C37C2
hypercenterC4D37
hypocenterC37D4
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C4

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 148

A minimal faithful permutation representation — 2 generators on 41 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);(2,4)(6,41)(7,40)(8,39)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Polycyclic presentation:

2^3,37|b^2=c,b^a=bc,d^a=d^36

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10596930, D296, #10596939, …
maximal normal subgroup of#10596930, D296, #10596939, …
maximal quotient of#10596930, D296, Dic148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(296, 6);