Finite Group Databasebeta

← Prev (#6600) Next (#6602) →

Cayley diagram

C4×D29 #6601

order232
isoclinismisoclinic class of D29
automorphismAut(G) = C22×AGL(1,𝔽29) (order 3248) · Inn(G) = D29 · Out(G) = C23×C7
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×D29

Splittings

FittingC4×C29 ⋊ C2
derived, SylowC29 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4D29
commutator, hypocenterC29C2×C4
FrattiniC2C2×D29
FittingC4×C29C2
socle, cosocleC2×C29C22
prime radicalC2×D29C2
LCSG ▷ C29
UCSC1 ◁ C4

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 116

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×D29, #90772, D29⋊C8, …
maximal normal subgroup ofC8×D29, #90772, D29⋊C8, …
maximal quotient ofC8×D29, #90772, C4×Dic29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(232, 5);