Finite Group Databasebeta

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Cayley diagram

C2×D93 #67321

order372
isoclinismisoclinic class of D93
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD186
direct productC2×D93
unambiguous semidirect product(C2×C3)⋊D31
unambiguous semidirect product(C2×C31)⋊D3

Splittings

Fitting, socleC2×C3×C31 ⋊ C2
derived, HallC3×C31 ⋊ C22
SylowC31 ⋊ C2×D3
SylowC3 ⋊ C2×D31

Subgroups

subgroupG/H
center, hypercenterC2D93
commutator, cosocle, hypocenterC3×C31C22
FrattiniC1G
Fitting, socleC2×C3×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 186

A minimal faithful permutation representation — 2 generators on 36 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);(4,5)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD93⋊C4, #10625225, #10625226, …
maximal normal subgroup ofD93⋊C4, #10625225, #10625226, …
maximal quotient ofDic186, C4×D93, D372, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(372, 14);