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Cayley diagram

C8×D23 #67261

order368
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C2

Aliases

direct productC8×D23

Splittings

FittingC8×C23 ⋊ C2
derived, SylowC23 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC8D23
commutator, hypocenterC23C2×C8
FrattiniC4C2×D23
FittingC8×C23C2
socleC2×C23C2×C4
prime radicalC2×D23C4
cosocleC4×C23C22
LCSG ▷ C23
UCSC1 ◁ C8

22 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 184

A minimal faithful permutation representation — 2 generators on 31 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)(24,25,26,28,27,29,30,31)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC16×D23, #10624980, C2×C8×D23, …
maximal normal subgroup ofC16×D23, #10624980, C2×C8×D23, …
maximal quotient ofC16×D23, #10624980, C8×Dic23, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(368, 3);