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Cayley diagram

C2×C4×D27 #88397

order432
isoclinismisoclinic class of D27
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D27

Splittings

FittingC2×C4×C27 ⋊ C2
derived, SylowC27 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4D27
commutator, hypocenterC27C22×C4
FrattiniC2×C9C22×D3
FittingC2×C4×C27C2
socleC22×C3C2×D9
prime radicalC22×D27C2
cosocleC2×C27C23
LCSG ▷ C27
UCSC1 ◁ C2×C4

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 216

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D27)⋊C8, C42×D27, #11720121, …
maximal normal subgroup of(C2×D27)⋊C8, C42×D27, #11720121, …
maximal quotient ofC4×Dic54, C42×D27, #11720121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 44);