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Cayley diagram

D4×D23 #67289

order368
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD4×D23

Splittings

FittingD4×C23 ⋊ C2
SylowC23 ⋊ C2×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×D23
commutator, socle, cosocleC2×C23C23
FittingD4×C23C2
hypercenterD4D23
hypocenterC23C2×D4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ D4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 92

A minimal faithful permutation representation — 3 generators on 27 points:

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

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×D23, #10625082, SD16×D23, …
maximal normal subgroup ofD8×D23, #10625082, SD16×D23, …
maximal quotient of#10625049, C22⋊C4×D23, (C22⋊D23)⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(368, 31);