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Cayley diagram

C2×Dic54 #88396

order432
isoclinismisoclinic class of Dic54
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic54
unambiguous semidirect product(C2×C27)⋊Q8

Splittings

SylowC27 ⋊ C2×Q8

Subgroups

subgroupG/H
centerC22C2×D27
commutator, cosocleC2×C27C23
FrattiniC2×C9C22×D3
FittingC2×C4×C27C2
socle, prime radicalC22×C3C2×D9
hypercenterC2×C4D27
hypocenterC27C2×Q8
LCSG ▷ C2×C27 ▷ C27
UCSC1 ◁ C22 ◁ C2×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 432

A minimal faithful permutation representation — 3 generators on 37 points:

(3,5,6,10)(4,7,8,9)(11,35,34,20,18,15,32,30,33,14,17,36,19,29,24,13,37,16,22,27,23,31,12,28,21,26,25);(1,2)(3,4,6,8)(5,9,10,7)(12,15)(13,19)(14,22)(16,17)(18,28)(20,21)(23,30)(24,29)(25,35)(26,34)(27,33)(31,32)(36,37);(1,2)

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11720049, #11720057, #11720063, …
maximal normal subgroup of#11720049, #11720057, #11720063, …
maximal quotient ofC4×Dic54, #11720118, #11720119, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 43);