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Cayley diagram

D4×D27 #88400

order432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD4×D27

Splittings

FittingD4×C27 ⋊ C2
SylowC27 ⋊ C2×D4

Subgroups

subgroupG/H
centerC2C22×D27
commutator, cosocleC2×C27C23
FrattiniC2×C9C22×D3
FittingD4×C27C2
socleC2×C3C22×D9
hypercenterD4D27
hypocenterC27C2×D4
LCSG ▷ C2×C27 ▷ C27
UCSC1 ◁ C2 ◁ D4

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 108

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×D27, #11720160, SD16×D27, …
maximal normal subgroup ofD8×D27, #11720160, SD16×D27, …
maximal quotient of#11720127, C22⋊C4×D27, #6171⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 47);