Finite Group Databasebeta

← Prev (#67285) Next (#67287) →

Cayley diagram

C2×C4×D23 #67286

order368
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D23

Splittings

FittingC2×C4×C23 ⋊ C2
derived, SylowC23 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4D23
commutator, hypocenterC23C22×C4
FrattiniC2C22×D23
FittingC2×C4×C23C2
socleC22×C23C22
prime radicalC22×D23C2
cosocleC2×C23C23
LCSG ▷ C23
UCSC1 ◁ C2×C4

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 184

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D23)⋊C8, C42×D23, #10625043, …
maximal normal subgroup of(C2×D23)⋊C8, C42×D23, #10625043, …
maximal quotient ofC4×Dic46, C42×D23, #10625043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(368, 28);